Optical Measuring Device and Process

ABSTRACT

An achromatic 3D STED measuring optical process and optical method, based on a conical diffraction effect or an effect of propagation of light in uniaxial crystals, including a cascade of at least two uniaxial or conical diffraction crystals creating, from a laser source, all of the light propagating along substantially the same optical path, from the output of an optical bank to the objective of a microscope. A spatial position of at least one luminous nano-emitter, structured object or a continuous distribution in a sample is determined. 
     Reconstruction of the sample and its spatial and/or temporal and/or spectral properties is treated as an inverse Bayesian problem leading to the definition of an a posteriori distribution, and a posteriori relationship combining, by virtue of the Bayes law, the probabilistic formulation of a noise model, and possible priors on a distribution of light created in the sample by projection.

INTRODUCTION

The present invention relates to an optical measuring method and device.It applies to all fields of imaging, in particular, though not limitedto, the field of Microscopy, including, but not limited to, the fieldsof Biology, Medicine, Pharmacy, Semiconductors, materials study,Metrology, control, measurement and observation and to all processes foracquisition of information from optical observations, in the macroscopicor microscopic field.

Many definitions, used for all this invention, are combined into a laterchapter: “Definitions and technical additions”.

Microscopy

An optical microscope is an instrument generally used to view, analyseor measure objects too small for the naked eye. Referring to FIG. 1,which shows an illustration of the paradigm of Microscopy, 100.

Optical microscopes including illumination, by a light source, notshown, using a microscope, 10, of a biological or non-biological sample,11, and the time-dependent measurement, using either visual observationor a detection module 12, of the light emitted, re-emitted, diffused orreflected or transmitted by the sample. In Biology, the sample comprisesa single—or a plurality—of different biological entities, 13 and 14,positioned at different positions. Examples of such objects are, amongothers, a cell, a virus, a protein or a DNA fragment. In artificialindustrial vision the sample can be, for example, a semi-conductorelement.

Microscopy is segmented into different modalities having differentcharacteristics and purposes. Many descriptions of the differentmodalities, their characteristics and their advantages exist extensivelyin the literature and are found for example on the company web sites ofZeiss, Leica, Nikon, or Olympus.

Microscopy applications can be segmented in different ways: one of theseis distinguishing the modalities of Microscopy for the displaying ofminuscule point sources of those allotted to the measure of continuousobjects.

The case of the minuscule point sources is a priori much simpler. Theobject consists of a small number of light points; the latter can bedescribed by a small number of parameters—the descriptors definedhereinbelow—greatly simplifying the physical problem and the algorithmiccomplexity. The case of a continuous object describes that spatialdistribution—or space-time, if the dynamic is considered—continuous, isdifferent and is also described in this patent application.

Fluorescence Microscopy

Fluorescence microscopy is one of the modalities of microscopy, it hasreplaced in many applications, the other microscopy techniques. Afluorescence microscope is an optical microscope used to studyproperties of objects or of organic or inorganic substances by using thephenomena of fluorescence instead of, or in addition to other modalitiessuch as reflection and absorption.

We refer again to FIG. 1, describing this time a fluorescence microscopeeither used in biology or artificial vision to characterize, forexample, materials; in fluorescence microscopy, tiny point sources, 15to 18, for example fluorophores, based on the physical phenomenon of onephoton fluorescence, are fixed at specific positions of predeterminedbiological objects, 13 and 14; the light emitted by the point sources isobserved instead of observing the light emitted by the objects, 13 and14, themselves.

The sample is illuminated by light of wavelength, or specificwavelengths, which is absorbed by the point sources, thereby inducingthe emission of light at different, higher, wavelengths. During thecollection of the light emitted by fluorescence, the illumination lightis separated from the emitted fluorescence, which is lower, by the useof a spectral emission filter.

Fluorescence Microscopy studies the light emitted by small pointsources, fluorophores. However, when the density of fluorophores ishigh, fluorophores are no longer analysed individually but treated as acontinuous object. It is important to note, from this stage, that thesame system enables observation of continuous objects, and is notlimited to the observation of point sources.

Fluorophores have become an important tool for the visualization ofbiological objects. The activity and the biological informationincluding details above the limit of resolution of 200-250 nm aresystematically viewed and measured using fluorescence microscopy. Thisresolution limit is derived from the Rayleigh criterion, which in thebest case, reaches 200-250 nm in systems designed specifically. For along time, until the emergence of superresolution techniques describedbelow, it was recognized that optical techniques, including fluorescencemicroscopy, are unable to visualize details smaller than the Rayleighcriterion, which is about 200-250 nm.

The main implementations of fluorescence microscopy, as described indetail in the literature, are the confocal microscope, often used in ascanning configuration or spinning disk configuration, and thewide-field imaging microscope.

Confocal Microscopy

Referring now to FIG. 2 which is a simplified representation of aconfocal fluorescence microscope of the prior art 200.

A confocal fluorescence microscope, FIG. 2 is an optical instrument. Itsmain hardware components are shown in FIG. 2. They include:

-   -   a light source, 20,    -   an optomechanical frame not shown    -   a cube filter, 21,    -   a microscope objective 22, and,    -   a detector assembly, 23,    -   a processing unit, not shown.

The light source 20, which may be an arc lamp or a laser, creates lightenergy necessary for fluorescence.

The Optomechanical frame, not shown, is the support of all the opticalcomponents and auxiliary optics and includes alignment capacities. Italso includes optical elements, not shown, capable of shaping the beamto allow its focus point of a minimum size by means of the microscopeobjective.

It can also comprise, in a confocal microscope having scanningfluorescence, a spatial or angular scanning mechanism, not shown, tochange the position of the point source with respect to the object to bemeasured.

The cube of filters, 21, channels the different optical signals andavoids contamination of the fluorescence signal by the excitation light.The cube is composed of filters: excitation filter, 210 dichroic mirror,211, and emission filter 212.

The microscope objective 22 focuses the light created by the source inthe focal plane of the objective lens 24, a light distribution patternof small size, and the light distribution considered as optimumconsisting of the Airy disk. The microscope objective 22, also collectsback fluorescent light emitted by the fluorophores.

For a confocal microscope having scanning fluorescence, the system canbe descanned, i.e., the return light can pass through the scanningmechanism to compensate for the translation due to scanning.

A detector lens, 25, creates, in the image plane of the detector 26, amagnified image of the focal plane of the objective lens 24.

A confocal hole, 27, is theoretically placed in the image plane of thedetector 26.

In most practical systems, the confocal hole, 27, is placed in anintermediate imaging plane, not shown, and reimaged onto the image planeof the detector 26.

The assembly of the detector, 23, detects the fluorescent intensity inthe overall illuminated volume, and converts it into digital signal. Fora confocal scanning microscope, the assembly of the detector consists ofa detector of a single element, such as a PMT or SPAD. For a confocalmicroscope with rotary disk, the assembly of the detector consists of amatrix of detector elements, such as a CCD, an EMCCD, a CMOS or a matrixof SPAD.

All components mounted from the light source to the dichroic filter arethe illumination path, 201. The detection channel, 202, represents allthe components mounted from the dichroic filter to the assembly of thedetector.

The elementary optical process of a standard confocal microscope can besegmented into six parts:

-   -   Projecting light on the volume analysed    -   Fluorescent light emission by fluorophores    -   Imaging of the fluorophores in the focal plane    -   Limitation in the focal plane of light analysed by confocal hole    -   Integration of light analysed by a photoelectric detector    -   Display of the measured intensity as a pixel value in an image.

Fluorescence microscopes are available from several manufacturers, suchas Nikon, Zeiss, Leica and Olympus. Fluorescence microscopes can beeither standard microscopes suitable for fluorescence or microscopesoptimised specifically for fluorescence. Modern microscopes areversatile instruments capable of operating in many different modalities,including, but not limited to, fluorescence modalities, using the sameoptomechanical platform and most of the components. Most fluorescencemicroscopes are developed as an open platform, capable of performingseveral additional features with minimal modifications. Otherfluorescence microscopes are instruments dedicated, adapted for aspecific task, such as medical or pharmaceutical diagnostic.

However, other fundamental biological activities also occur at scalessmaller than 200 nm in biological samples. At this level of spatialresolution, important phenomena can be observed: the biologicalprocesses at the scale of intracellular, cell information transfer, thefolding and unfolding of the proteins and changes in the DNA and RNA.Thus, for example, the measurement of this intracellular informationopens new avenues for understanding biological activity, and leads toprogress in understanding and monitoring of research and medicaldiagnostic.

However, the different existing methods of microscopy and existingmicroscopes, not incorporating the superresolution, allow microscopicobservation up to the optical diffraction limit. This reduces theirfield of use to a limited set of applications.

Superresolution

New optical methods, the superresolution methods, are capable ofobtaining images at a resolution greater than the diffraction limit.These methods are being developed by several companies, laboratories andresearchers and some of the instruments using these methods, thesuperresolution microscopes, are commercially available. A synthesis ofsuperrsolution techniques was published by the Swedish Academy ofSciences, on the occasion of the award of the Nobel Prize in Chemistry2014 [38]. Several comparative analyses of superresolution methods haverecently been published in the literature, as the articles bySchermelleh et al. [1].

An updated bibliography on the superresolution is on the website of thecompany Zeiss, and on the website of the company Nikon.

New superresolution techniques obtain information beyond the resolutionlimit. The main problem of all existing superresolution techniques isthat the envelope limit of the performance, expressed in terms ofresolution, lateral and longitudinal, speed, light intensity necessary,and phototoxicity in the biological object, and therefore of ability tomeasure different biological objects. This point has also beenemphasized by Eric Betzig during his class presentation at the awardsceremony of the Nobel Prize in Chemistry 2014.

In addition, most of the methods and instruments can providesuperresolution either a good lateral resolution or a good longitudinalresolution, but rarely both.

In addition, all these instruments are complex and require a highlyskilled operator.

In addition, these instruments can generally observe a small part ofbiological specimens because of strong operational limitations, such as,for some of them, a shallow depth of field or a requirement of very highlight intensities, harmful to cells.

Another problem with the methods and instruments of superresolution, isthat most of them are able to recover in the illuminated volume, theattributes of a single fluorophore, but fail to recognize the presenceof simultaneously several fluorophores and measuring their attributes.

An additional problem with certain existing methods and instruments ofsuperresolution is that these methods and instruments are presented tousers and perceived by them as a general tool, able to replace thestandard or confocal microscopes. However, existing superresolutionmethods and instruments lack the simplicity, robustness, ease of use andare expensive relative to the standard microscopes, which hinders theiruse as research tools or as general diagnostic tools.

Another problem with certain existing superresolution methods and toolsis that most of these methods and tools are designed as stand-aloneinstruments designed to replace standard microscopes. Such an approachrequires the replacement of existing instruments and the renewal of allsystems and devices all the knowledge and know-how related to microscopyplatforms and developed over many years.

Another problem with most methods and fluorescence microscopyinstruments and superresolution is that these methods and tools aredesigned on a paradigm of image acquisition, the entity for which basicinformation is—either more images, or—or more—ROI regions—bi- orthree-dimensional Region Of Interest. Algorithmic, systemic andsuperresolution methods described later in the context of the inventionwill, by their inherent flexibility, the development of new strategiesof acquisition. These acquisition procedures, dynamic and selective,will be defined by optimised sequence acquisition and interactive anddeferred processing. They allow a more sophisticated optimisation ofuseful information, as defined by criteria based on the shape, geometryand dynamics of one or more fluorescent objects, separately or relativeone to the other.

Another problem with the majority of existing methods and instruments offluorescence microscopy and superresolution is that these methods andinstruments are designed for studying samples on microscope slides.However, the confocal microscope is used today in many medical fields asan instrument of in-vivo diagnosis for internal and externalexaminations on the human body by means of fiber optics used toilluminate and display fluorescence emitted by tissue to be diagnosed.Superresolution does not currently perform such in-vivo diagnostics.Algorithmic, systemic and superresolution methods described later in thecontext of the invention will allow the development of novel methods ofin-vivo diagnostics which will reduce the need to take biopsies and willshorten wait times for patients.

So there is still an urgent need to provide superresolution methods andtools and algorithm methods capable of measuring an object or abiological stage with high accuracy.

SUMMARY OF THE INVENTION

A first aspect of the invention relates to an optical measuring devicefor determining the spatial distribution or the location of re-emittingsources on a sample, the sample comprising at least one re-emittingsource, excited by light and re-emitting light according to a lawdetermined as a function of light projected on the sample, the devicecomprising

an achromatic projection module, containing a laser, whereof thewavelength is aligned to the excitation wavelength of said at least onere-emitting source, to create either a compact light distribution or asequence of compact light distributions of different topology

a scanning module for scanning the sample optically,

a detection module for detecting the light re-emitted by said at leastone re-emitting source of the sample for the or for each of the compactlight distributions of different topology and for each of the scanningpoints of the sample;

an image acquisition module for acquiring for each scanning point eitheran image or a sequence of images, for the sequence of images, each imagecorresponding to one of the compact light distributions of differenttopologies,

an algorithm module in which formulation of the reconstruction of thesample and of its spatial and/or temporal and/or spectral properties isconsidered as a reverse Bayesian problem and leads to the definition ofa distribution a posteriori.

By way of the Bayes law, a law a posteriori can combine theprobabilistic formulation of a noise model, as well as any a priori on alight distribution created in the sample by projection.

In an embodiment, the algorithm module is configured for

estimating the light distribution in the sample by the use of clouds ofspecific emitters which favours sparse solutions;

estimating the average a posteriori, and

representing the results, based on the average a posteriori, either inthe form of an image or in the form of digital or graphic data.

According to an embodiment the estimation of the average a posteriori isperformed by means of an algorithm of Monte-Carlo Markov Chain (MCMC)type.

Another aspect of the invention relates to an optical measuring devicefor determining spatial distribution or location of re-emitting sourceson a sample, the sample comprising at least one re-emitting source,excited by the light and re-emitting light as per a law determined as afunction of the light projected on the sample, the device comprising

an achromatic projection module, containing a laser, whereof thewavelength is aligned to the excitation wavelength of said at least onere-emitting source, to create either a compact light distribution or asequence of compact light distributions of different topology,

a scanning module for scanning the sample optically, integrated or notinto the device,

a detection module for detecting the light re-emitted by said at leastone re-emitting source of the sample for the or for each of the compactlight distributions of different topology and for each of the scanningpoints of the object;

an image acquisition module for acquiring for each scanning point eitheran image or a sequence of images for the sequence of images, each imagecorresponding to one of the compact light distributions of differenttopologies,

a module of MAP algorithm not regularized with positivity restrictionfor processing data and reconstructing the sample,

the representation of results based on the results of the MAP algorithm,either in the form of an image or in the form of digital or graphicdata.

According to an embodiment, the MAP algorithm also contains a frequencyband limitation restriction.

According to an embodiment, the MAP algorithm uses an accelerateddigital diagram of Nesterov type.

According to an embodiment for a sequence of images, the redundancy inthe frequency information is used, due to the different frequencycharacteristics of the different distributions projected on the sample,for compensating and considerably reducing the impact of missing pointsor scanning irregularities.

According to an embodiment, the MAP algorithm is adapted to resolve aninverse problem relating to a sum of a small number of terms, such as alow-frequency component and a more sparse component.

According to an embodiment, the MAP algorithm is adapted to impose anon-local redundancy restriction of the solution, for example bycalculating weights on the images or on the different digital masks andthe non-local tree of similarities being applied to the solution asregularization.

According to an embodiment, a mask of variable size is used in the planeof the detector to obtain images having either different axialcharacteristics, or different or optimised rejection capacities ofparasite light, overall or locally.

According to an embodiment, a computer program is configured forexecuting the embodiments described previously.

Another aspect of the invention relates to an optical measuring processfor determining the spatial distribution or the location of re-emittingsources on a sample, the sample comprising at least one re-emittingsource, excited by the light and re-emitting light as per a lawdetermined as a function of light projected on the sample, the processcomprising

achromatic projection by a laser whereof the wavelength is aligned tothe excitation wavelength of said at least one re-emitting source tocreate either a compact light distribution or a sequence of compactlight distributions of different topology,

optical scanning of the sample,

detection of the light re-emitted by said at least one re-emittingsource of the sample for the or for each of the compact lightdistributions of different topology and for each of the scanning pointsof the sample;

image acquisition for acquiring for each scanning point either an imageor a sequence of images, for the sequence of images each imagecorresponding to one of the compact light distributions of differenttopologies,

application of an algorithm in which formulation of the reconstructionof the sample and its spatial and/or temporal and/or spectral propertiesis considered as a reverse Bayesian problem and leads to the definitionof a distribution a posteriori.

By way of the Bayes law a law a posteriori can combine the probabilisticformulation of a noise model, as well as any a priori on a lightdistribution created in the sample by projection.

In an embodiment the algorithm comprises

estimating the light distribution in the sample by the use of clouds ofspecific emitters which favour sparse solutions; and

estimating the average a posteriori,

representing the results based on the average a posteriori either in theform of an image or in the form of digital or graphic data.

According to an embodiment, the estimation of the average a posterioriis performed by means of an algorithm of Monte-Carlo Markov Chain (MCMC)type.

Another aspect of the invention relates to an optical measuring processfor determining the spatial distribution or the location of re-emittingsources on a sample, the sample comprising at least one re-emittingsource, excited by the light and re-emitting of the light as per a lawdetermined as a function of the light projected on the sample, theprocess comprising

achromatic projection by a laser whereof the wavelength is aligned tothe excitation wavelength of said at least one re-emitting source, tocreate either a compact light distribution or a sequence of compactlight distributions of different topology,

optical scanning of the sample,

detection of the light re-emitted by said at least one re-emittingsource of the sample for the or for each of the compact lightdistributions of different topology and for each of the scanning pointsof the sample;

image acquisition for acquiring for each scanning point either an imageor a sequence of images, for the sequence of images, each imagecorresponding to one of the compact light distributions of differenttopologies,

application of MAP algorithm not regularized with positivityrestriction,

representation of results based on the results of the MAP algorithmeither in the form of an image or in the form of digital or graphicdata.

According to an embodiment, the MAP algorithm also contains a frequencyband limitation restriction.

According to an embodiment the MAP algorithm uses an accelerated digitaldiagram of Nesterov type.

According to an embodiment for a sequence of images, redundancy in theinformation frequency is used due to the different frequencycharacteristics of the different distributions projected on the sample,for compensating and considerably reducing the impact of missing pointsor scanning irregularities.

According to an embodiment the MAP algorithm is adapted to resolve aninverse problem relating to a sum of a small number of terms, such as alow-frequency component and a more sparse component.

According to an embodiment the MAP algorithm is adapted to impose anon-local redundancy restriction of the solution, for example bycalculating weights on the images or on the different digital masks andthe tree of non-local similarities being applied to the solution asregularization.

According to an embodiment a mask of variable size is used in the planeof the detector to obtain images having either different axialcharacteristics, or different or optimised rejection capacities ofparasite light, overall or locally.

According to an embodiment, a computer program is configured to executethe embodiments described previously.

In another embodiment of this invention, an optical measuring process isused to determine the spatial distribution or the location ofre-emitting sources on a sample, the sample comprising at least onere-emitting source, said at least one re-emitting source re-emittinglight as a function of light projected on the sample, as per adetermined law, by a first light source comprising a first laser,whereof the wavelength is aligned to the excitation wavelength of there-emitting source and the re-emitting source which can be depleted oractivated by the action of one or more light sources, comprising atleast one second laser whereof the wavelength is aligned to thedepletion or activation wavelength of said re-emitting source, theprocess comprising:

the two compact light distributions spreading along the same opticalpath for all lasers,

the compact light distribution of the first excitation laser being of aregular topological family, ideally a Gaussian distribution or an Airyspot,

the compact light distribution of the depletion or activation laserconsisting of superposition of a singular distribution, of vortex type,on a first polarization, linear or circular, and of a distribution knownas black sphere or “top-hat” on the polarization orthogonal to the firstpolarization,

said compact light distributions being created by a cascade of at leasttwo crystals of conical diffraction, or a set of uniaxial crystals,optionally separated by a control element of chromatic polarization ornot, dynamic or static,

detection of the light re-emitted by said at least one re-emittingsource of the sample;

generation of at least one image, from the detected light; and

direct detection or algorithmic analysis of the images to obtain spatialdistribution information or location of said at least one re-emittingsource.

In a particular arrangement of the previous embodiment of thisinvention, the polarization control element described is an opticalelement consisting of a set of one or two achromatic quarter-waves and achromatic wave plate, the whole being designed such that the opticalelement creates, between the two conical crystals or between twouniaxial crystals, a difference in rotation of the polarization betweenthe excitation beam and the depletion beam close to 180 degrees and notdiffering by more than 30 degrees from this value.

In a particular arrangement of the previous embodiment of thisinvention, the polarization control element is an optical elementwhereof the material has a property of optical activity and thethickness of the optical element is selected such that the naturaldispersion of the optical activity of the material creates, between thetwo conical crystals or between two uniaxial crystals, a difference inrotation of the polarization between the excitation beam and thedepletion beam close to 180 degrees and not differing by more than 30degrees of this value.

In a particular arrangement of the previous embodiment of thisinvention, no polarization control element is used, but the two conicalcrystals are made of different material and the natural dispersion ofthese two materials compensates the conical diffraction approximately atthe excitation wavelength and not at the depletion wavelength.

In another embodiment of this invention, an optical device is used todetermine the spatial distribution or the location of re-emittingsources on a sample, the sample comprising at least one re-emittingsource, said at least one re-emitting source re-emitting light as afunction of light projected on the sample, as per a determined law, by afirst light source comprising a first laser, whereof the wavelength isaligned to the excitation wavelength of the re-emitting source and there-emitting source which can be depleted or activated by the action ofone or more light source(s), comprising at least one second laser,whereof the wavelength is aligned to the depletion or activationwavelength of said re-emitting source, the process comprising:

the two compact light distributions spreading along the same opticalpath for all lasers,

the compact light distribution of the first excitation laser being of aregular topological family, ideally a Gaussian distribution or an Airyspot,

the compact light distribution of the depletion or activation laserconsisting of superposition of a singular distribution, of vortex type,on a first polarization, linear or circular, and of a distribution knownas black sphere or “top-hat” on the polarization orthogonal to the firstpolarization,

said compact light distributions being created by a cascade of at leasttwo crystals of conical diffraction, or a set of uniaxial crystals,optionally separated by a control element of chromatic polarization ornot, dynamic or static,

detection of the light re-emitted by said at least one re-emittingsource of the sample,

generation of at least one image, from the detected light; and

direct detection or algorithmic analysis of the images to obtain spatialdistribution information or location of said at least one re-emittingsource.

In a particular arrangement of the previous embodiment of thisinvention, the polarization control element described is an opticalelement consisting of a set of one or two achromatic quarter-waves and achromatic wave blade, the whole being designed such that the opticalelement creates, between the two conical crystals or between twouniaxial crystals, a difference in rotation of the polarization betweenthe excitation beam and the depletion beam close to 180 degrees and notdiffering by more than 30 degrees from this value.

In a particular arrangement of the previous embodiment of thisinvention, the polarization control element is an optical elementwhereof the material has a property of optical activity and thethickness of the optical element is selected such that the naturaldispersion of the activity optical of the material creates, between thetwo conical crystals or between two uniaxial crystals, a difference inrotation of the polarization between the excitation beam and thedepletion beam close to 180 degrees and not differing by more than 30degrees from this value.

In a particular arrangement of the previous embodiment of thisinvention, no polarization control element is used, but the two conicalcrystals are made of different material and the natural dispersion ofthese two materials compensates the conical diffraction approximately atthe excitation wavelength and not at the depletion wavelength.

Another implementation of this invention describes an optical method forlocally evaluating the spherical aberration in each place of the sample,or each place of the object being imaged, by using conical diffractionand its phase and polarization effects. The sample is illuminated withuneven light distribution, which can be for example but non-limiting, ablack sphere (or top hat) such that 3D distribution presents two lobesof the same intensity below and above the focal plane. In the presenceof spherical aberration in the system these two lobes are not of thesame intensity. This effect can be used to take an image, in particulara confocal image, by illuminating above and below the focal plane (byuncoupling the illumination and the imagery). By then analysing theintensity ratio of the two images, the quantity of spherical aberrationof the system can be deduced therefrom.

Another implementation of this invention describes an optical device forlocally evaluating the spherical aberration in each place of the sample,or each place of the object being imaged, by using conical diffractionand its phase and polarization effects. The sample is illuminated withuneven light distribution which can be for example but non-limiting, ablack sphere (or top hat) such that 3D distribution presents two lobesof the same intensity below and above the focal plane. In the presenceof spherical aberration in the system these two lobes are not of thesame intensity. This effect can be used to take an image, in particulara confocal image, by illuminating above and below the focal plane (byuncoupling the illumination and the imagery). By then analysing theintensity ratio of the two images, the quantity of spherical aberrationof the system can be deduced therefrom.

Another implementation of this invention describes an optical method forlocally evaluating the spherical aberration in each place of the sample,or each place of the object being imaged, by using conical diffractionand its phase and polarization effects. Forming a light beam by conicaldiffraction via a cascade of crystals produces a distribution ofintensity connected directly to the spherical aberration. Thisdistribution can be obtained, for example but non-limiting, betweencrossed linear polarizers and two biaxial crystals whereof the opticalaxes are aligned. A half-wave plate is inserted between the twocrystals. By way of characteristic form this distribution will be called“four-leaf-clover”. In the absence of spherical aberration, thisdistribution comprises four lobes perfectly equal and all at the samefocus. The spherical aberration caused by an optical system breaks thesymmetry of this distribution at the same time in the focus and thedistribution of intensity in the four lobes. Fine measuring of the valueof spherical aberration is possible by an offset estimator of focus oflobes and ratios of intensity at different focal planes.

Another implementation of this invention describes an optical device forlocally evaluating the spherical aberration in each place of the sample,or each place of the object being imaged, by using the conicaldiffraction and its phase and polarization effects. Forming a light beamby conical diffraction via a cascade of crystals produces a distributionof intensity connected directly to the spherical aberration. Thisdistribution can be obtained, for example but non-limiting, betweencrossed linear polarizers and two biaxial crystals whereof the opticalaxes are aligned. A half-wave plate is inserted between the twocrystals. By way of characteristic form, this distribution will becalled “four-leaf clover”. In the absence of spherical aberration, thisdistribution comprises four lobes perfectly equal and all at the samefocus. The spherical aberration caused by an optical system breaks thesymmetry of this distribution at the same time in the focus anddistribution of intensity in the four lobes. Fine measuring of the valueof spherical aberration is possible by an offset estimator of focus oflobes and ratios of intensity on different planes of focus.

Another implementation of this invention describes an optical method forcalibrating in real time a beam scanning system by point monitoringgenerated by a laser diode in near infrared. An optical method isexecuted for monitoring in real time on a camera a point scanned by abeam scanning system (galvanometric mirrors, bidirectionalpiezo-electric mirror or any other system). Using a wavelength in thenear infrared dispenses with chromatic effects of optics which makesthis system useable for calibrating several wavelengths projected in aconfocal microscope. Also, using a laser diode in the near infraredensures that low passage of the calibrating laser in the microscope willhave a highly marginal effect only, the wavelength being far greaterthan the usual excitation wavelengths of fluorescence.

Another implementation of this invention describes an optical device forcalibrating in real time a beam scanning system by point monitoringgenerated by a laser diode in near infrared. An optical method isexecuted for monitoring in real time on a camera a point scanned by abeam scanning system (galvanometric mirrors, bidirectionalpiezo-electric mirror or any other system). Using a wavelength in thenear infrared dispenses with chromatic effects of optics which makesthis system useable for calibrating several wavelengths projected in aconfocal microscope. Also, using a laser diode in the near infraredensures that low passage of the calibrating laser in the microscope willhave a highly marginal effect only, the wavelength being far greaterthan the usual excitation wavelengths of fluorescence.

Another implementation of this invention describes an optical method,modified Wollaston prism, for duplicating a set of light distributionswithout modifying the relationships between them, which can be used interms of the methods described in this invention or within the scope ofSTED methods described in this invention or other standard STED methods.Using several Wollaston prisms in cascade can separate an incident beaminto many emerging beams. The same effect can be obtained by modifyingthe Wollaston prism, to create the composed Wollaston prism, by addingto it pieces of uniaxial crystal whereof the index and orientation ofthe birefringence are suitably selected. In this way a prism can be madefrom a single block of uniaxial crystal which can separate an incidentbeam into 2^(n) emerging beams (for example eight or sixteen) which arecontained in one plane and separated by equal angles. Once focused onthe sample, the result is 2^(n) points aligned and equally separated. Ifthe incident beam has passed through a LatSRC module, these 2^(n) pointsare not 2^(n) Airy patches, but the distributions created by the moduleare all identical. The advantage of using this beam splitter is to scanthe sample faster since there are 2^(n) light points in place of asingle one.

Another implementation of this invention describes an optical device,modified Wollaston prism, for duplicating a set of light distributionswithout modifying the relationships between them, which can be used interms of the devices described in this invention or within the scope ofSTED device described in this invention or other standard STED devices.Using several Wollaston prisms in cascade, it is thus possible toseparate an incident beam into a large number of emerging beams. Thesame effect can be obtained by modifying the Wollaston prism to createthe composed Wollaston prism by adding pieces of uniaxial crystalwhereof the index and orientation of the birefringence are suitablyselected. In this way a prism can be made from a single block ofuniaxial crystal which can separate an incident beam into 2^(n) emergingbeams (for example eight or sixteen), which are contained in one planeand separated by equal angles. Once focused on the sample, the result is2n points aligned and equally separated. If the incident beam has passedthrough a LatSRC module, these 2^(n) points are not 2^(n) Airy patches,but the distributions created by the module are all identical. Theadvantage of using this beam splitter is to scan the sample faster sincethere are 2^(n) light points in place of a single one.

Another implementation of this invention describes an optical method,and an optical procedure using a property of Poisson noise forgenerating from a realisation of a Poisson VAR of parameter I (average),two independent realisations of a Poisson VAR of parameter I/2, becauseof processing a posteriori. Due to a process for generation of random orpseudo-random numbers, a binomial law is simulated. Analysis orreconstruction of the two measurements generated in this way, calledSplit Photon method, provides two independent results in terms ofprobabilities, and the differences between these two results illustratedependence on the reconstruction algorithm relative to the measuringnoise. Using a local comparison criterion of these two reconstructions,when there is a significant difference between the two reconstructedimages or signals, it is possible to apply locally or overall differentparameters in the reconstruction algorithm applied to the originalmeasurements. It is also possible to use another algorithm such as a MAPalgorithm with restriction of overall or local regularity by using thesimilarity map or any other comparison criterion to optimise theregularization parameter(s). It is also possible to consider thesimilarity map or of the criterion used in the Split Photon method,graphically or digitally, to illustrate local or overall dependence onreconstruction to the measuring noise. It is also possible to generate,rather than a couple of measurements, an n-tuple of measurements, byusing a multinomial law of parameters rather than a binomial law.

Finally, it is possible to iterate the Split Photon method by generatingseveral couples or n-tuples of measurements, still by processing aposteriori of measurements, but by modifying the grain in thepseudo-random generator.

Another implementation of this invention describes an optical device,and an algorithmic device using a property of Poisson noise forgenerating from a realisation of a Poisson VAR of parameter I (average),two independent realisations of a Poisson VAR of parameter I/2, by wayof processing a posteriori. Because of a generation process of random orpseudo-random numbers a binomial law is simulated. The analysis orreconstruction of the two measurements generated in this way, calledSplit Photon method, provides two independent results in terms of theprobabilities, and the differences between these two results illustratethe dependence of the reconstruction algorithm on the measuring noise.By using a local comparison criterion of these two reconstructions, whenthere is a significant difference between the two reconstructed imagesor signals, it is possible to locally or overall apply differentparameters in the reconstruction algorithm applied to the originalmeasurements. It is also possible to use another algorithm such as a MAPalgorithm with overall or local regularity restriction, by using thesimilarity map or any other comparison criterion to optimise theregularization parameter or the regularization parameters. It is alsopossible to consider the similarity map or of the criterion used in theSplit Photon method, graphically or digitally, to illustrate the localor overall dependence of the reconstruction at the measuring noise. Itis also possible to generate, rather than a couple of measurements, ann-tuple of measurements by using rather than a binomial law, amultinomial parameter law. Finally, it is possible to iterate the SplitPhoton method by generating several couples or n-tuples of measurements,still by processing a posteriori of measurements, but by modifying thegrain in the pseudo-random generator.

Another implementation of this invention describes an optical method andan algorithmic method using the ICE algorithm, which replace calculationof the expectancy of the law a posteriori effected by LSE via iterationof explicit calculation of the average of the law a posteriori of apixel conditionally to its neighbours.

Another implementation of this invention describes an optical device andan algorithmic device using the ICE algorithm which replaces thecalculation of the expectancy of the law a posteriori effected by LSEvia iteration of the explicit calculation of the average of the law aposteriori of a pixel conditionally to its neighbours.

Another implementation of this invention describes an optical method,and an algorithmic method for measuring the signal proportion whichbelongs to the region of interest (pinhole), for each image Thismeasurement, called Pinhole Ratio, consists of comparing in a spatialregion of the object the proportion of photons which are resent andimages in the region of interest of each image issue of this regionrelative to the total number of photons resent by the object in allimages considered. This ratio gives information locally on the nature ofthe object image. In the event where the Pinhole Ratio deviates from theabove value it is possible to modify the characteristics of thereconstruction algorithm.

Another implementation of this invention describes an optical device,and an algorithmic device for measuring the signal proportion whichbelongs to the region of interest (pinhole), for each image Thismeasurement, called Pinhole Ratio, consists of comparing in a spatialregion of the object the proportion of photons which are resent andimages in the region of interest of each image coming from this regionrelative to the total number of photons resent by the object in allimages considered. This ratio gives information locally on the nature ofthe object image. In the event where the Pinhole Ratio deviates from theabove value it is possible to modify the characteristics of thereconstruction algorithm.

Another implementation of this invention describes an optical method,and an algorithmic method for measuring the position of the emitter byusing the particular features of distributions called offset half-moons,described in this invention, by using an appropriate optical method, bymeasuring the intensity ratio between the lobes. This 3D location can beused either in projection, i.e., by projecting one or more distributionswith offset half-moons on the object and by using an adapted algorithm,for example the algorithms described in this invention, or in emissionby having light sent by the emitter pass through an optical modulecreating this distribution and by analysing the return PSF.

Another implementation of this invention describes an optical device,and an algorithmic device for measuring the position of the emitter byusing the particular features of distributions called offset half-moons,described in this invention, by using an appropriate optical device, bymeasuring the intensity ratio between the lobes. This 3D location can beused either in projection, i.e., by projecting one or more distributionswith offset half-moons on the object and by using an adapted algorithm,for example the algorithms described in this invention, or in emissionby having light sent by the emitter pass through an optical modulecreating this distribution and by analysing the return PSF.

Another implementation of this invention describes an optical method,and an algorithmic method for measuring the position of the emitter byusing the particular features of distributions called “dark helix”,described in this invention, by using an appropriate optical method, bymeasuring the angle of the axis connecting the two zeros. This 3Dlocation can be used either in projection, i.e., by projecting one ormore distributions with offset half-moons on the object and by using anadapted algorithm, for example the algorithms described in thisinvention, or in emission by having light sent by the emitter passthrough an optical module creating this distribution and by analysingthe return PSF.

Another implementation of this invention describes an optical device,and an algorithmic device for measuring the position of the emitter byusing the particular features of distributions called “dark helix”,described in this invention, by using an appropriate optical device, bymeasuring the angle of the axis connecting the two zeros. This 3Dlocation can be used either in projection, i.e., by projecting one ormore distributions with offset half-moons on the object and by using anadapted algorithm, for example the algorithms described in thisinvention, or in emission by having light sent by the emitter passthrough an optical module creating this distribution and by analysingthe return PSF.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in connection with certainembodiments with reference to the following illustrative figures so thatit can be better understood.

With specific reference to the figures, it is emphasized that theindications represented are presented as an example and for purposes ofillustrative discussion of the embodiments of the invention and arepresented only in order to provide what is considered to be thedescription of the most useful and easy to understand principles andconceptual aspects of the invention. In this regard, no attempt is madeto show structural details of the invention in more detail than isnecessary for a fundamental understanding of the invention, thedescription taken with the drawings making apparent to those skilled inthe art how the several forms of the invention may be embodied inpractice.

In the drawings:

FIG. 1 is a simplified view of a confocal fluorescence microscope of theprior art also used as support of the invention;

FIG. 2 is a simplified pictorial representation of a fluorescencemicroscopy system;

FIG. 3 is a simplified schematic illustration of a conical diffractionmodule in accordance with one embodiment of the present invention;

FIGS. 4a to 4f are simplified pictorial representations of themeasurement paradigms and containment volume according to embodiments ofthe invention and of the confocal microscopy;

FIG. 5 is a simplified pictorial representation of a particularembodiment of the SRCDP microscopy platform;

FIG. 6a is a simplified schematic illustration of a module lateralsuperresolution in accordance with an embodiment of the presentinvention;

FIG. 6b is a simplified schematic illustration of another embodiment ofa lateral superresolution module, according to an embodiment of thepresent invention;

FIGS. 7a to 7c shows tables of light distributions of a conicaldiffraction module according to the polarization of the polarizers ofthe input and output for several values of the parameter of conicaldiffraction, ρ₀. These light distributions were calculated by simulationof equations developed by Berry, [2]; FIG. 7d complete these dispatchtables by presenting the variation of distributions called offsethalf-moons depending on the axial position (z-axis); FIG. 7e shows a newdistribution “dark helix” comprising two zeros, the axis connecting thetwo zeros rotates depending on the spread;

FIG. 8 is a simplified schematic illustration of one of the embodimentsof dark tracking;

FIG. 9 is a simplified schematic illustration of a method forsuperresolution algorithm of fluorophores data, in accordance with anembodiment of the present invention;

FIG. 10 is a simplified schematic illustration of the calculation ofdescriptors;

FIG. 11 is a simplified schematic illustration of the control module ofthe SRCDP platform.

FIG. 12 shows the light distribution obtained, “Four-leaf-clover”distribution in different spherical aberration values.

In all the figures, like reference numerals identify like parts.

DEFINITIONS AND TECHNICAL SUPPLEMENTS

We use the term biological to describe any biological entity in LifeScience, regardless of its origin, human, animal or plant and thepurpose of his observation, research, diagnosis or treatment. This termincludes the medical uses of the technique described. Microscopy is usedin the field of biology, for example, to observe, study and measurebiological entities (objects) and their dynamics.

By extension, the term artificial Vision will be used to describe allmeasuring applications, Metrology or observation of objects or elementsproduced or constructed or made by a human being or machine, forexample, to observe, study and measure Semiconductors or to characterisematerials.

The usual definitions are used for the description: phase andpolarization, polarimetry, vectors and Jones matrices, Stokes parametersand measurement techniques Stokes and Jones parameters.

The usual definitions are used for: optical diffraction limit, Rayleighcriterion, Airy disk and its radius and diameter. We use in the contextof the invention, the terms of superresolution, superresolved,superresolution imaging and superresolution microscopy to describeoptical data acquisition, optical imaging, microscopy and artificialvision at a resolution higher than the optical diffraction limit. Theusual definitions are used for fluorescence and for fluorophores.

The terms longitudinal and axial will be used alternatively to describethe dependence of the light along the axis of propagation, which isreferred to as the axis z or longitudinal axis. The term lateral will beused to describe the dependence of light in the axes orthogonal to theoptical axis of the system, referred to as the axes x and y.

The usual definitions are used in the description for the mode TEM₀₀ ofa fiber and the English terms, “Photonic Crystal Fiber”—PCF—, “few modesfiber”—FMF, vortex Fiber and “dual core Photonic Crystal Fiber” forspecific fibers.

Reference is made to a device for coupling several lasers havingdifferent wavelengths or the same wavelength, with the same polarizationor with different polarizations, in one or more fiber optics, using theterm laser bank.

The definition of superoscillations is that by Yakir Aaronov and SirMichael Berry. Superoscillation is a phenomenon in which a signal whichis limited overall in bandwidth can contain local segments whichoscillate faster than its fastest Fourier components. [26]

The centre or centroid of a light distribution is the centre of gravityof the intensity. The diameter of a light distribution is the diameterof the first zero intensity, both for regular and singular waves,without taking into account the central zero of a singular wave.

Two light distributions are collocated if their centres coincide or areseparated by a low spatial value relative to the dimension of thedistribution of light.

In this patent application, we use the emission wavelength, as the basicmetric system.

In this patent application, the usual definitions are used for thefollowing optical components: lens whose definition has been broadenedto include all optical means which transmit, refract or reflect thelight, auxiliary optics—optical sub-module to interface and adjusteither the geometric parameters or the parameters of phase and/orpolarization between two other optical sub-modules or modules—,polarizer, analyser, retardation plate, beam splitter, polarizing andnon-polarizing, beam combiner, polarizing and non-polarizing.

In this patent application, the usual definitions are used for azimuthaland radial polarizers. This means, implicitly or explicitly, somedevelopments described later for azimuthal and radial polarizers, allpolarizing elements variable in space.

In this patent application, the usual definitions, [3] and [38], areused for different superresolution techniques; these techniques can becombined into families:

-   -   REversible Saturable OpticaL Fluorescence Transitions (RESOLFT),        combining the techniques: Stimulated Emission Depletion        microscopy (STED), Ground state depletion (GSD), Saturated        Structured Illumination Microscopy (SSIM) and SPEM (Saturated        Pattern Excitation Microscopy), Localisation Microscopy,        combining the techniques of Photoactivated localization        microscopy (PALM), FPALM (3D Localization in Fluorescence        Photoactivation Localization Microscopy), Stochastic optical        reconstruction microscopy (STORM), dSTORM (direct STORM), SPDM        (Spectral Precision Distance Microscopy), “stochastic blinking”,        Ground state depletion (GSD), and similar techniques        (irrespective of the acronym used)    -   Structured Image Microscopy (SIM)    -   FRAP (Fluorescence Recovery After Photobleaching),    -   TIRF (Total Internal Reflection Fluorescence Microscopy).

In this patent application, the usual definitions are used for differenttechniques of Microscopy, standard resolution or superresolution,fluorescent or not, such as “Computational Microscopy”, “CorrelativeMicroscopy”, “Cross-platform-microscopy, FCS—Fluorescence CorrelationSpectroscopy”, FCCS—“Fluorescence Cross-Correlation Spectroscopy”, orPCH—Photon Counting Histogram, RICS “Raster Imaging CorrelationSpectroscopy” or FRAP—“Fluorescence Recovery after Photobleachinganalysis”.

In this patent application, the usual definitions are used for the HoughTransform, for the MAP algorithms—“Maximum A Posteriori estimation”, LSE“Least Squares Estimation”, ICE “Iterated Conditional Expectation”.Reference is made to the E-LSE algorithm, “Emitter-Least Square Error3 anew algorithm described in this patent application.

We refer to a partial polarizer to describe a component or a modulewhose absorption is different for the two linear polarizations—lineardichroism—or for the two circular polarizations—circular dichroism.

We refer to dynamic polarization or phase elements, to describe theoptical means, which polarization or phase varies over time in acontrolled manner, discrete or continuous.

These dynamic polarization or phase elements include, but are notlimited to: rotating on their axes wave plate, light valves based onliquid crystal technology, electro-optical devices, also known asPockels cells, Kerr cells, for example by using components of PLZTmaterial, electro-optical resonant devices, magneto-optic devices, alsoknown as Faraday cells, acousto-optic or elasto-optic devices or anycombination of these means.

Reference is made to dispersive polarization or phase elements todescribe elements whereof the polarization state depends on thewavelength. The simplest of the dispersive polarization sub-modules isthe multimode or thick wave plate.

We refer to “centroid algorithm” to describe the standard procedure formeasuring the centroid and possibly the width (FWHM—Full width HalfMaximum) of a light distribution.

In this document, the usual definitions are used for followingoptoelectronic components: photoelectric detector, CCD, EMCCD, CMOS,SPAD—Single Photon Avalanche Diode and SPAD matrix.

We use the terms:

-   -   optical image for the spatial distribution of light intensity,    -   electronic image to describe the spatial distribution of charges        of a CCD, of current for a CMOS, of events or for a SPAD,        created by the optical image, at a given moment, in a detection        plane,    -   digital image to describe a matrix of numbers created by        conversion of the electronic image.

To simplify the reading and understanding of the text we will use theterm image to the output of a single pixel detector such as PMT or SPAD,considering it as an image consisting of a single pixel.

Where no ambiguity exists, or where the distinction between the threetypes of images is not necessary, we will use the simplified genericterm of image.

For the images is used the terminology used for the matrix detectors,such as CCD, EMCCD and CMOS. For SPAD and SPAD arrays, the measurementresult is an ordered list in time of photons impact detailing, for eachphoton, the time of impact and the position of the impact. To simplifythe presentation of this document, we will include this case in ourdefinition of images.

The images described in this document, in many cases, may becharacterized as microimages, images of size substantially equal to asmall number of the Airy disk diameters, typically less than 5diameters, and/or low number of pixels, typically 4*4 to 32*32.

In a digital image Aj, the indices m and n represent the indices of thepixels, and the origin of the pixels will be selected as the projectionof the centre of the analysis volume defined in a later paragraph.

Stokes Vectors Polarimetry

Polarimetry refers to the measurement of the polarization state ofincident light. The polarization state of the incident light can bedescribed by the Stokes parameters, a set of values introduced by GeorgeGabriel Stokes in 1852 and used in optics.

Copropagation of Two Optical Beams

Many systems and optical devices uses two beams—or more—having differentproperties. The beams can interact or not, or be projected sequentiallyor simultaneously. In the majority of these systems and devices, the twooptical paths are separated physically from each other. This physicalseparation creates, at the level of engineering of the system a set ofconstraints, which although resolvable, substantially emphasise thecomplexity of the system and its cost. Reference is made to systems ofcommon path, to reference a set of devices in which the twodifferentiated beams spread along the same physical path, at minorvariations.

In this invention, by extension, reference will be made to systems ofalmost common path to reference a set of devices in which the twodifferentiated beams spread along the same physical path but separateand rejoin in an optical module, the optical path in the optical elementbeing negligible relative to the total optical path. This definitionintroduces the case of an optical module, containing a polarizationseparator monitored at a short distance by an element combining the twopolarizations, or any similar element. The introduction of such a moduledoes not significantly modify the functionality and the advantages of acommon path system. Throughout this invention, for clearer understandingwhen a common path system is referred to it will include the case of analmost common path system.

Electric Field in Polar Coordinates and Angular Modes

E(ρ,θ)=A(ρ,θ)×exp[i φ(ρ,θ)]u(ρ,θ)   (EQ. 1)

It is customary in Optics to decompose the field components, i.e. itsamplitude, phase and polarization in orthogonal modes, Cartesian orpolar.

Many decompositions in orthogonal polar modes, such as Gaussian,Hermite-Gaussian, HGG and “Elegant” and Laguerre-Gaussian modes, areknown to those skilled in the art.

We mainly use in this paper, the decomposition of the amplitude of thefield.

Singular Waves

This research topic in optics, initiated by the seminal article by J. FNye and M. Berry in 1974 [4], is now known as “singular optics”.Examples of regular and singular waves are presented in the following.

The term beam shaping is used to describe the transformation of a wavein given form and topology into a wave of another form or topology, andin particular transformation of a regular wave into a singular and viceversa.

Topology and Compact Light Distributions

A point-source light distribution will be considered compact if itsatisfies one of the conditions of compactness defined below, as twoalternative and not exclusive conditions:

-   -   either more than 75% of the energy is contained in a circle of        radius less than 1.75 times the radius of Airy,    -   or a light domain, defined by a line of zero intensity and        containing more than 65% of the energy is within a circle of        radius less than twice the radius of Airy,

We distinguish different families of point light distributions, ofdifferent topologies:

Regular distributions in their usual definition in Optics,

Singular distributions or waves, otherwise known as optical vortices, oftopological charge (azimuthal order) l, where the phase varies from 0 to2 πl, around the direction of propagation, l being an integer,

Amplitude distributions with azimuthal variation of order l, alsoreferred to as Laguerre-Gaussian distribution,

Polarization, and optionally phase distributions, with azimuthalvariation of order l, referred to as radially polarized Laguerre-Gaussmodes.

Two compact light distributions will be deemed being of differenttopological families if they meet at least one, and any of the followingconditions:

One is regular and the other is singular,

One is point-source and the other is a ring-source,

Azimuthal orders l of the amplitude of the two different lightdistributions differ,

Azimuthal orders l of the polarization or the phase of the two differentlight distributions differ.

Alternatively, two light distributions projected onto a given volumewill be considered of different topologies if a significant portion ofthe surface illuminated together, the gradients are of reverseddirection.

Light Nanoemitters

A light nanoemitter is a small secondary emitter attached to an object,and it is significantly smaller than a fraction of a wavelength,typically but not limited to a size smaller than one fifth of thewavelength; a light nanoemitter absorbs the incident energy and re-emitslight at the same wavelength as the incident light or differentwavelengths; the light emitted by the nanoemitter may be coherent,partially coherent or incoherent with the absorbed light. The mainexamples of nanoemitters are fluorophores and nanoparticles, but alsoinclude many other elements.

The definition in the context of the invention of nanoemitters light isdetermined by the following two conditions:

creating a secondary point-source light emitter, and

predetermined positioning of the emitter with respect to an artificial,biological or organic entity.

The physical mechanisms that can create a nanoemitter are numerous, andinclude but are not limited to absorption, scattering or reflection,fluorescence, emission-depletion, [5], for example using RESOLFT, photoactivation phenomena and photo depletion techniques, fluorescence of twoor more photons, or non-elastic scattering, Raman scattering, or anyother physical mechanisms known to those skilled in the art. We use theterm light emission to describe the emission of electromagnetic waves bya light nanoemitter, the light being coherent, incoherent or partiallycoherent.

We extend our definition of nanoemitters by including scatteringparticles, absorbent or reflective, attached to a biological or organicentity; the action of a scattering, diffusing, reflecting or absorbingparticle on the electromagnetic field can indeed be described, for anabsorbing particle, following Babinet's principle, as a creation, with areverse phase of an auxiliary secondary field emerging from theparticle, superimposed on the incident electromagnetic field.

We refer to in this patent application to descriptors of a singlenanoemitter to denote the set of information describing a nanoemitter asa point source at a given moment. Since the nanoemitter is considered asa point source, all the information representing it contains a limitednumber of parameters, namely: its position in space, its intensity, itsspectral characteristics of the intensity, coherence, phase andpolarization of the light emitted by the fluorophore as a function ofthe incident light.

Reference is made in this patent application to the descriptors of astructured object. For example, for a uniform line, all of theinformation representing it contains a limited number of parameters,either its orientation in space, its intensity, spectralcharacteristics, intensity, coherence, phase and polarization of thelight emitted by the object, as a function of incident light.

For continuous distribution, the object is represented, as usual inimage processing, by a matrix of intensities.

However, in most cases, and in the description of the invention, werefer, under the designation of descriptors, a subset of descriptors ofa nanoemitter or of a single geometric object, including its geometricposition, its intensity, and the type of fluorophore, whether severalpopulations of light nanoemitters, differentiated for example by theiremission spectrum, are present in the same sample. This simplificationused in the description does not alter the scope of the invention whichwill include in its scope all the descriptors of light nanoemitters.

To simplify the understanding of the context of the invention, thefollowing description refers only the simplest case, one in which thenanoemitter is a fluorophore and physical interaction is the one photonfluorescence. However, this description should be understood as asimplified illustration of a general description of the methods andconcepts applicable to all light nanoemitters mentioned previously orknown to those skilled in the art, regardless of the underlying physicalphenomenon.

It is striking that the nanoemitter samples the incident light intensityfield at a three-dimensional position accurately without influence ofthe complete spatial distribution of the incident intensity. We willreference this remarkable property in this patent application as thesampling ability of light nanoemitter.

However, the embodiment of the invention as described also measuresstructured objects and continuous distributions having no samplingcapacity of the light nanoemitter.

We refer again to the FIG. 1 which represents a set of nanoemitters orstructured objects positioned on a given biological object, 15 and 16 onthe one hand and 17 and 18 on the other hand. Alternatively, the lightemitted can consist of continuous distribution, not shown in FIG. 1, orin any combination of nanoemitters, structured objects or continuousdistributions. The set of nanoemitters, structured objects or continuousdistributions is referenced as a set “bright biological objects”, theyrepresent a map of the biological object, in the sense defined by AlfredKorzybski in general semantics. However, it is common practice tosimplify the description, reference the object as theluminous-biological object itself, when no ambiguity can arise. Theluminous biological object contains information that is relevant to thebiological object, mainly spatiotemporal information, the objectposition and orientation with respect to time, and morphologicalinformation, for example in the case of division of a cell in two.

The measurement system according to at least one embodiment of theinvention will calculate the measured map, and carry out evaluation ofthe descriptors of any combination of nanoemitters, structured objectsor evaluation of the spatial distribution of continuous distributions.This measured map differs from the original map, due to noise,measurement conditions, the system limits or measurement uncertainty.This information of the measured map can be developed later intodifferent levels of abstraction. This first level of abstraction, whichpresents the results of direct measurement, contains a priori nobiological information but is the results of a physical measurementdescribed by nanoemitters, by structured objects or by continuousdistributions which could also represent any marked entity.

The second level, the geometric level of abstraction, structuresnanoemitters of structured objects or continuous distributions in theform of geometric objects. It comprises a description of luminousobjects and their dynamic characteristics, such as their position ororientation, or their morphology. At this level, the information isstill physical and geometric information describing a set of objects.The geometrical information uses the measured card and auxiliaryinformation, potentially external to the system, the relation betweenlight spots and objects.

The biological level of abstraction, allows some understanding of thebiological reality through a constitutive relationship between objectsmeasured and corresponding biological entities. It contains a set ofinformation on the biological object, mainly the position and itsdynamics, its shape and morphology. The biological information uses themeasured card and the geometrical information and auxiliary information,potentially external to the system, the relation of the light spots andobjects with biological entities. A number of conclusions on thebiological functionality of the sample can be obtained at this level.

The level of functional abstraction allows apprehension of thebiological reality. It consists of functional information, decorrelatedfrom geometric information, and responding to interrogations in termsand biological jargon, such as: “has the virus penetrated the cell?”.

An additional level of information can be defined including the controland instrumentation process; in fact, a more evolved control andinstrumentation process can be defined to reach more structuredbiological information, via automation of the process of dataacquisition. An example of such processes is described by StevenFinkbeiner, under the name of “Robotic Microscopy Systems”.

This description of levels of abstraction, defined in this application,has been redacted, for the sake of simplicity, for Biology. It isapplicable, mutatis mutandis, to all fields of Vision, biological andmedical, artificial and industrial.

Conic Diffraction

Conical diffraction or refraction is an optical phenomenon predicted byHamilton [6] in 1832, and two months later confirmed experimentally byLloyd [7]. Conical diffraction describes the propagation of a light beamin the direction of the optical axis of a biaxial crystal.

In fact, in a biaxial crystal, the optical axis is positioned in theplane created by the crystallographic axes x and z; the angle relativeto the axe z is θ₀, depending on the three indices of refraction as perthe law,

${\tan \; \theta_{0}} = {\sqrt{\frac{n_{1}^{- 2} - n_{2}^{- 2}}{n_{2}^{- 2} - n_{3}^{- 2}}}.}$

Hamilton predicted that the light emerges in the form of a hollow coneof rays. Conical refraction is an important phase in the history ofscience and has played a role in the demonstration of the theory ofelectromagnetic waves.

A renewed interest in the conical diffraction occurred in the last yearsof the twentieth century has led to a complete theory by Berry et al.[2], validated experimentally in 2009 [8]. Here we follow the theory,terminology and definitions of Berry, including, from this point, thename change of the physical effect, using the more rigorous term ofconical diffraction.

However, it is important to note that the term “conical diffraction” isalso used for two other techniques not relating to the technique wedescribe:

-   -   Oblique incidence diffraction is also called conical diffraction    -   “Conical diffraction mounting” references mounting a diffraction        network in which the network is mounted on a curved surface.

Conical diffraction has attracted considerable theoretical andexperimental, but “no practical application seems to have been found”,[9].

Historically, conical diffraction was observed in biaxial crystals. Werefer to a conical crystal to describe a biaxial crystal inorganic ororganic, exhibiting the phenomenon of conical diffraction. Somenon-limiting examples of biaxial crystals include Aragonite, KTP, KTA,KBiW, LBO, KNbO3, MDT, YCOB, BIBO, DAST, POM, NPP, LAP, and LiInS2LiInSe2.

Other effects exist, creating either inherently weaker conicaldiffraction effects or creating slighter conical diffraction along ashorter optical path. However, these effects can be used within thescope of the devices described. These effects include polymers, liquidcrystals and induced externally birefringence effects. The polymersinclude but are not limited to: stretched polymer sheets and cascadepolymerisation, [10]; liquid crystals include but are not limited to:thermotropic biaxial nematic phase, [11]; the external effects inducedbirefringence include, but are not limited to: applying an electricfield creating an electro-optical effect on a non-centrosymmetric cubiccrystal, and the photo-elastic modulator.

The phase in the vortex created by conical diffraction is a geometricphase and is therefore intrinsically achromatic.

The additional chromatic effects are dispersion of the optical axis anddependence on the different parameters present in the equations ofconical diffraction as a function of the wavelength.

The dispersion chromatic of the optical axis creates an angle of theoptical axis of the crystal, dependent on the wavelength, relative tothe optical axis of the system. It is due, in the majority of cases, todispersion of the refraction indices.

The refraction indices depend on the wavelength, as per Sellmeierequations. The angle of the optical axis varies therefore as a functionof the wavelength, and it creates an angle of chromatic inclination ofthe optical axis in the plane created by the crystallographic axes x andz.

It depends considerably on the type of crystal. In an MDT crystal, theleast dispersive crystal in the visible spectrum, the direction of theoptical axis varies by less than 0.1 degrees between 540 nm and 700 nm.In a KTP crystal, the most achromatic crystal in the telecommunicationIR, the angle varies by 0.05 degrees, between 1.350 nm and 2.100 nm, andless than 0.02 degrees on the telecommunication window—1450 nm to 1650nm. On the other hand, angle θ₀ can vary considerably as a function ofthe wavelength in some organic crystals such as DAST.

The compensation of chromatic dispersion of the optical axis can becarried out using the geometric optic. The chromatic dispersion of thedirection of the optical axis can be compensated by using the naturaldispersion of glass or other optical materials, or by using networks orprisms. The achromatisation procedure does not differ, in this case,from the standard procedure of correction of any chromatic aberration ongeometric optics. This procedure can be designed and optimised using oneof the commercial optical software packages available in definingadequate target functions.

A different achromatisation concept is based on the use of two differentmaterials, having effects of inverse conical diffractions, at high andlow chromatic dispersions.

The dependence of different parameters present in the equations ofconical diffraction as a function of wavelength modifies the parametersof efficacy of the effects of conical diffraction.

For conical linear crystals, defined later, the fundamental transferfunction is identical to the unit and trivially independent ofwavelength. By contrast, the vortex transfer function depends on thewavelength and can be shown by a chromatic factor equal to τ (λ).

For sinusoidal conical crystals, defined later, the behaviour isdifferent to that of conical linear crystals: the fundamental wavedepends on the wavelength and the wave vortex is almost independant ofthe latter. In fact, simulations show that the form of the wave vortexis modified only slightly by a variation of the parameter, θ₀ from 0.5to 0.75. By contrast, the form of the fundamental wave depends onwavelength and this effect must be taken into account in the design ofsystems using the two waves, fundamental and vortex.

We refer now to FIG. 3, which is a simplified schematic illustration ofa configuration of a conical diffraction module 300, in accordance withan embodiment of the present invention.

Incident light, 30, is assumed to be collimated, although otherconditions can be adapted using simple optical means.

The setup itself comprises a first lens 31, a conical crystal 32 and anoptional lens 33. The first two lenses 31 and 33 are preferablyconfigured in the form of a Kepler telescope 1:1. The numerical apertureof the first lens 31 in the image space, represented below by U₀,determines the parameters of the conical [diffraction] effect throughthe conical radius, defined below. An imaging plane conical, 35, isplaced in the focal plane of the first lens 31, a polarizer or a partialpolarizer part 29, described above, may also be added. However, in someoptical systems where incident light is already polarized this elementis unnecessary. A focusing lens, 36, determines the size of the finallight spot. It can be a microscope objective external or can be mergedwith the second lens 33, as implemented in another embodiment of thisinvention. The distribution of the light projected on the sample is in afirst approximation, neglecting the vectorial effects, a reduced imageof the light distribution in the image plane. The influence of vectorialeffects will be discussed below. The scale ratio or the magnification isdetermined by a microscope objective.

Given the spatial variable, R, the conical imaging plane, and the wavevector, U, represented by cylindrical coordinates R, θ_(R) and U, θ_(U)and given λ, the wavelength of light.

The behaviour of the electric field emerging from the conical crystal 32is fully characterized by a single parameter, the radius conical R₀; theconical radius depends on the material and the thickness of the crystal.

We introduce standardized parameters for the description below of thelight distribution, to be valid in both conical imaging plane and at thefocus of the microscope objective, in the limits of the scalar theory ofdiffraction. An example of introduction of the standardised parametersis described in reference [2].

The normalized radial position, ρ, the wave vector normalized, u,represented by cylindrical coordinates by ρ, θ_(R) and u, θ_(U), and thenormalized radius conical ρ₀ are given by:

$\begin{matrix}{{\rho = {2\frac{R}{\lambda}U_{0}}},{{u = \frac{U}{U_{0}}};{\rho_{0} = {2\frac{R_{0}}{\lambda}U_{0}}}}} & \left( {{EQ}.\mspace{14mu} 2} \right)\end{matrix}$

U₀ is the numerical aperture of the system.

Different regimes exist for all volumic optical diffraction effects ofminimal interaction. The volumic diffraction effects of minimalinteraction have the following properties:

-   -   modification of incident light is created by perturbation of        Maxwell equations,    -   the scale of the interaction far greater than the wavelength,        typically over 10 μm.

The fact that these different regimes create totally different opticaleffects has been studied mainly for acousto-optical interactions, but ispresent in all optical effects, including conical diffraction.Terminology adapted from works by Raman on acousto-optics will be usedand the following cases will be differentiated:

ρ₀≦1, linear Raman Nath regime, referenced earlier, [37], “linear thinconical crystal”, in which a simple surface approximation of the effectcan be used,

ρ₀<1 and >0.5, sinusoidal Raman Nath regime, referenced earlier, [37],“sinusoidal thin conical crystal”, in which a surface approximation ofthe effect can be used,

ρ₀<3 and >1, intermediate regime, referenced earlier, [37], “averageconical crystal”, in which complex effects couple the effects of RamanNath regimes and the Hamilton-Lloyd regime to be described later on,

ρ_(0≧3,) regime to be called Hamilton-Lloyd regime referenced earlier,[37], under the name of “thick crystal”, similar to the Bragg regime inacousto-optics, in which the effects described by Hamilton and Lloyd arepresent. Only the crystals of the Hamilton-Lloyd regime, or thickconical crystals, ρ₀≧3, can be described by the Hamilton theory and havethe particular feature of spreading beams inside the crystal in the formof an “obscure cone”, or “conefringent”, diffracting in the form of acone, a term used by some authors.

Since 1832 Hamilton [6] had already noted this condition on theamplitude of the effect of biaxial crystals, necessary for validity ofhis description of conical refraction, by showing the necessity of“sufficient biaxial energy”.

“29 New consequences of Fresnel's principles. It follows from thoseprinciples, that crystals of sufficient biaxial energy ought to exhibittwo kinds of conical refraction, an external and an internal: a cusp-raygiving an external cone of rays, and a normal of circular contact beingconnected with an internal cone”.

The wave emerging crystal thin conical, E(ρ, θ_(R)), expressed innormalized coordinates for a wave circularly polarized, is constitutedby the superposition of two waves, referred to herein as the fundamentalwave, E_(F) (ρ), a regular wave, and vortex wave, E_(V) (ρ,θ_(R)), asingular wave; these two waves are coherent one with another,collocated, and circularly polarized with an inverse direction ofchirality:

$\begin{matrix}{{E\left( {\rho,\theta_{R}} \right)} = {{{E_{F}(\rho)} + {E_{V}\left( {\rho,\theta_{R}} \right)}} = {{{E_{F}(\rho)}\begin{pmatrix}1 \\{- i}\end{pmatrix}} + {{F_{V}(\rho)}{\exp \left( {{- i}\; \theta_{R}} \right)}\begin{pmatrix}1 \\i\end{pmatrix}}}}} & \left( {{EQ}.\mspace{14mu} 3} \right)\end{matrix}$

In this equation, E_(F) (ρ) is the scalar fundamental amplitude, F_(V)(ρ) is the reduced scalar magnitude of vortex and they are given by:

E _(F)(ρ)=2π∫oƒu cos(ρ₀ ,u)J ₀(ρu); F _(V)(ρ)=2π∫oƒu sin(ρ₀ u)J ₁(ρu).  (EQ. 4)

For a thin linear conical crystal, the fundamental wave can beapproximated by an Airy disk and the vortex wave can be approximated toa linear vortex, represented by:

F _(V)(ρ)=2πρ₀ ∫oƒu ² J ₁(ρu).   (EQ. 5)

Assuming that the action of partial polarizer, 29, is the scaling of thevortex wave by a parameter α, the Stokes parameters can be deduced fromthe above equations, β being the angle of the linear polarization:

S ₀=(E _(F)(ρ))²+(α² F _(V)(ρ))²

S ₁=2αE _(F)(ρ)F _(V)(ρ) sin θ_(R) ; S ₂=2αE _(F)(ρ)F _(V)(ρ) cos θ_(R);

S ₃=(E _(F)(ρ))²−(α² F _(V)(ρ))²

β=θ_(R);  (EQ. 6)

As described previously, the wave emerging from the conical crystal, fora wave polarized circularly, consists of superposition of two waves, thefundamental wave, a regular wave, and the vortex wave, a singular wave.All incident beams of homogeneous polarization can be decomposed on theorthogonal base composed of circular right and circular leftpolarizations. The incident beam is therefore the coherent superpositionof two beams, one polarized in circular right polarization and thesecond in circular left polarization. The emerging beam is the coherentsuperposition of four beams; two fundamental waves, the first created bythe beam polarized in circular right polarization and the second by thebeam polarized in circular left polarization and two vortex wavescreated by the beams polarized in circular right and left polarization.However, if the two fundamental waves have the same spatial distributionand can interfere but retain their topology, the two vortices haveopposite chiralities and create complex distributions. Differentcombinations of these waves can be made by selecting polarizations atinput and output, which produces PSF of different forms.

Sparse Object

We use the terms of “sparse object” to describe either a set of sparseemitters, or parsimonious, specific light emitters, or a set of sparseobjects, sparsity being defined in the references [41-43] and not beinglimited to specific objects but including filaments, for example. Forsparse emitters, the selected limit is a number less than twelve,positioned in a volume whose size in each dimension is less than 3wavelengths, at the wavelength of transmission or at the wavelength ofthe reflection of the emitters. The volume of a size less than 3wavelengths that contains the sparse object is referred to as ananalysis volume of reduced size.

We will use the term of continuous object to describe a set of lightpoint or continuous emitters which do not fulfil the conditionsdescribed earlier in the definition of the sparse object. The transitionbetween these two regimes is not straightforward and many experimentalcases will be intermediate cases between these two types of object.

We refer now to FIGS. 4a to 4 c, which are a simplified representationof the concept of volumic containment in the confocal microscope.

The functionality of the volumic containment is limited in all threespatial dimensions, the observed region of the sample volume to a sizeas small as possible, analysis volume. The functionality of the volumiccontainment limits the analysis volume by the combination of twoeffects: the confinement of the light projected onto a small area,ideally the size of the Airy spot, 50, and the elimination of defocusedlight by the confocal hole, 28, of FIG. 2. The superposition of thesetwo effects creates a small volume, the analysis volume, 60. This volumedetermines the size of the elementary region detected by the system.

Consider a sparse or continuous object, 51, consisting of a plurality ofnanoemitters, 53 to 59. The nanoemitters from 53 to 55 positioned in thetest volume 60, and only they are both excited by the light source andthe photons emitted by them arrive at the detector module. Thenanoemitters not located in the cone of illumination, 56 and 57 are notilluminated by the incident light. The light emitted by the nanoemitters58 and 59, located at the conjugate plane of the confocal hole, 28 ofFIG. 2, is blocked almost entirely by the confocal hole, 28 FIG. 2.

Two different Cartesian coordinates are defined in the system, FIG. 4 c:

The reference “i”: The axes referenced “i” represent a Cartesianreference system centred on the centre of the analysis volume, 61.

The reference “a”: the axes referenced “a” represents a Cartesianreference centred for each light nanoemitter on the nanoemitterconsidered as a discrete point, 62.

When using another embodiment of the invention, described later, if avortex is projected on the sample being analysed, the centre of thevortex will be generally defined as the centre of the analysis volume.

At least one embodiment of the invention uses conical diffraction torealize the fundamental optical modules of the technique. However,alternative implementations, replacing the modules based on conicaldiffraction by modules based on other optical concepts, are able toprovide the same functionality. They are intrinsically part of the scopeof this invention. Alternative optical concepts include but are notlimited to uniaxial crystals, sub wavelength gratings, structured lasermodes, holographic components and other techniques known to thoseskilled in the art.

The concepts, techniques and optical and optoelectronic devices aredescribed for example in the book written by D. Goldstein, “PolarizedLight”, [12], the “Handbook of Confocal Microscopy”, [13], “Handbook ofOptics”, [14].

Optical Semaphore

In this embodiment of the invention we use the term optical semaphore todescribe an optical, passive or active element capable of channellingincident light to different channels or detectors as a function of aproperty of light. The simplest case is a dichroic blade which separatesthe light into two channels as a function of wavelength.

In this embodiment of the invention we use the term, “Position dependentOptical Semaphore”—PDOS—or optical semaphore dependent on position—todescribe an optical semaphore which channels light as a function of theposition of the emitter point. The PDOS will be determined by a seriesof transfer functions, Ti(x,y,z) dependent, for each channel or detectori, on the position of the emitter (x,y,z), in a reference volume. Theorder of the PDOS will be the number of channels or detectors. The PDOSwill be “lossless”, in an analysis volume, if the sum of the transferfunction, Ti(x,y,z) is equal to the unit in the analysis volume.

The confocal hole, described by Minsky, [15], could be considered inthis embodiment of the invention as a degenerated PDOS of order 1.

In the majority of cases dependence of the PDOS is a complex function ofthe lateral and longitudinal positions. However, in embodiments of theinvention we use the term, “Longitudinal Position dependent OpticalSemaphore”—LPDOS—or optical semaphore dependent on the longitudinalposition—to describe an optical semaphore which channels light as afunction of the longitudinal position of the emitter point. The LPDOSwill be determine by a series of transfer functions, Ti(z) dependent,for each channel or detector i, on the longitudinal position of theemitter (z), in a reference volume. The order of the PDOS will be thenumber of channels or detectors. The LPDOS will be often coupled to astop, limiting the lateral field of the system.

Transmission by Fiber Optics

A main use of fiber optics is the exclusive transmission of the TEM₀₀mode. However, some configurations of fiber optics such as FMF or vortexFibers, mainly but not exclusively based on fibers called “PhotonicCrystal Fiber”—PCF—and fibers called “vortex fiber allow simultaneoustransmission or not of more complex modes, including vortex modes,having equal vorticity or less than 2. It would therefore be possible todeport the optical distributions created by conical diffraction by meansof fiber optics, allowing major simplification of the optical system.

The possibility of deporting the optical distributions created byconical refraction by means of fiber optics allows application of theembodiments of the invention to many additional applications, forexample but not limited to gastric or gastroenterological observation,and to observation of the colon and urinary tracts.

Also, some fibers “dual-core photonic crystal fibers”, [16], allowinteraction between two modes, one of them being a vortex, and providingan additional physical mechanism to create diversified transferfunctions.

Measurements of Several Wavelengths

In embodiments of the invention, the object can be lit by monochromaticlight and by using for example a classic laser or a monochromatic lamp.Also, in some configurations a broad-spectrum laser—called “white laser”can be used. This configuration is simple, since one of the mainparameters of the system is fixed and clearly determined. However, inother embodiments of the invention the object can also be lit by severalwavelengths, either discretely using several lasers for example, orcontinuously using a lamp or a laser having a wider spectrum forexample.

Many existing superresolution systems measure simultaneously orsequentially at several wavelengths. In fact, it is possible to marksimilar or different elements with fluorophores having differentspectral, responses so they can be recognised and separated. It isimportant to present the two different cases:

-   -   The use of fluorescent markers, emitting at two different        wavelengths, excited by the same wavelength;    -   The use of fluorescent markers emitting at two different        wavelengths or the like, excited by two different wavelengths.

It should be noted that in the case of the use of fluorescent markers,emitting at two different wavelengths, excited by the same wavelength,the problem of recalibration between the measurements of a wavelengthrelative to the second, are intrinsically inexistent since thesuperresolution position information is derivative of the projection oflight, which is perfectly identical for the different wavelengths.

This allows relative calibration of the position of fluorophores at twodifferent wavelengths, with precision limited only by the experimentalcalibration system, eliminating the major problem of recalibrationbetween two images of different wavelength.

The possibility of achromatising optical systems based on conicaldiffraction makes a tool of choice for implementation of opticalsystems, of common path, in many applications, and more particularly forembodiments of the invention described.

Achromatisation is also possible for optical systems based on uniaxialcrystals, and for almost all alternative implementations of thisinvention, with, for each of them, almost more or less substantialcomplexity.

Other existing fluorescence systems uses light having a wider spectralcontent to reduce artefacts, and principally the effects of speckle.

Equally, the spectral properties of fluorescent proteins measure thepotential of intracellular molecular interactions by using the Försterenergy transfer technique—Förster (Fluorescence) Resonance EnergyTransfer (FRET).

In some implementations of PSIT systems the light of an incident laserbeam or beams is separated by means of a light separator into two beams,the main beam which will accomplish the functionality of the PSIT systemand an additional low-intensity beam used to measure the position of thelaser beam by means of a camera or a position detector. This devicemeasures highly precisely and in real time the position of the laserindependently of any wobble error or other mechanical error.

Information A Priori and Complementary Information

Embodiments of the invention described enable integration and merging ofadditional information external to the platform described, optical orcontextual, to obtain improvement in precision of information taken fromthe sample for any one of the cited levels of abstraction: map, thegeometric level of abstraction, the biological level of abstraction andthe functional level of abstraction.

More generally, spectral diversity, information obtained at severalwavelengths, polarization diversity, and information obtained byprojecting different states of polarization, expands the extent ofavailable information.

The fact that the absence of energy, for example in the case of the zeroof the vortex, is pertinent information, opens additional possibilitiesto the acquisition of information without “cost” in a number of photons.This situation has major importance for detection of low fluorescencephenomena, such as for example self-fluorescence.

One of the modalities described for some embodiments of the inventionwill be referenced by the name dark tracking.

We introduce the concept of optical integral information, informationwhich could be retrieved from optical measurements or by electromagneticwaves, on a target, by an observer, from a given viewpoint. Thisinformation contains many parameters of the object, related to itsposition, the materials which comprise it, its temperature, or itsorientation.

Optical integral information on the contrary does not containinformation on regions of the object having no optical path to theobserver, for example an element positioned in an opaque box, orphysical information which has no optical transcription.

Superresolved Measurements and Diffraction Limit

It has been long considered that optics intrinsically limited resolutionof any optical system, via the diffraction limit. The appearance ofsuperresolution techniques—in different fields and under differentnames—has shown that it is possible to exceed this diffraction limit, bydifferent means.

Embodiments described in this invention, such as detection of thepresence of two points of the same intensity, by projection of a vortexat the centre of gravity of light distribution created by thefundamental wave, are not limited in resolution a priori and couldideally—with an infinite number of photons—obtain any resolution, aswill be described later for a specific case.

Use of Non-Linear Interactions in Superresolution and Family of RESOLFTand STED Techniques

The use of non-linear interactions in a material medium between twolight beams was proposed in 1994 by Hell, [5] and [17], as the basis ofa superresolution system. Many different techniques flowed from theworks of Hell to create several families of techniques, such as RESOLFTand “localization microscopy”. Several reviews of these techniques havebeen published ([1] or [38]).

These non-linear interactions include, though are not limited to,interaction phenomena having two photons, emission-depletion, blinkingand photoactivation effects on which are based the RESOLFT technologyfamily and the family of “localization microscopy” technologies.

The family of RESOLFT technologies is well known and is described inseveral references, such as the article initial by Hell [5] and theinitial patent [17], or by Schermelleh et al. [1], or in recentpublications, Vicidomini et al. [18], or by Willig et al. [19].

In the STED technique described in the initial article by Hell [5], twobeams are projected sequentially onto the object: a standard excitationbeam, modelled in most cases by distribution of light described by anAiry function, and a depletion beam—having a doughnut or vortex form;the effect of depletion is to prevent fluorescence of fluorophores foundon the surface of the distribution of depletion light, but not modifyingemission of fluorophores positioned at the centre of the distribution oflight outside the distribution of depletion light; this createsdistribution of equivalent emission light smaller than the distributionof initial excitation light. This technique has produced equivalentdistributions of emission light of very small size, but needingconsiderable light depletion energies.

Several variants of STED have been developed: “CW STED”, [20], “gatedSTED”, [21], and “modulated STED”, [22]. In CW STED the pulsed laserused in the first version of STED is replaced by a simpler continuouslaser. In “gated STED” emitted photons are discriminated as a functionof their emission time for moving away emitted photons from fluorophoresnot having received during enough time the depletion beam; “modulatedSTED” uses an excitation beam modulated in intensity, in combinationwith synchronous detection dependent on modulation frequency. Thisdiscriminates the signal fluorescence created by the excitation beam ofthe residual fluorescence caused by the depletion beam.

Another variant, proposed by Gould et al. [45], uses a SLM for creatingeither separately or jointly the lateral and/or axial depletiondistributions.

The doughnut—or vortex—was created in the first version of STED by meansof a phase plate spatially varying. This implementation requires the useof two separate optical paths for the two beams, the excitation beam andthe depletion beam. This optical assembly is complex, highly dependenton any mechanical derivative and creates complex optical alignments. Theupdated system needs technical strength and the cost of the system ishigh. Also, this implementation is chromatic, as the phase plate adaptedto a wavelength no longer will be to another wavelength. With theoptical system not being achromatic, the use of STED having twodepletion wavelengths needs an even more complex optical system.

To simplify implementing the STED, several authors have proposedsolutions for producing a STED in which the two beams, the excitationbeam and the depletion beam would spread along the same optical path:

-   -   Wildanger et al. have proposed a STED Microscope with common        optical path, insensitive to the mechanical derivative, based on        properties of dispersion of different optical materials, [23],        This technology is marketed under the name EasyDONUT by the        company Abberior [28].    -   Bokhor et al. [24], propose the use of chromatic annular        separation of prealigned beams; however this solution blocks        some of the depletion light,    -   Hoeffman [25], proposes the use of a module containing the        prealigned optical elements creating the vortex in the optical        path of the depletion laser to simplify alignment,    -   Menon et al. [26], propose diffractive lenses for creating        zeroes of amplitude without phase singularities,    -   Reuss et al. [27] introduce a device for beam formation placed        directly opposite the objective lens. This device is based on        the use of birefringent crystals, mounted in the form of a        segmented wave plate, consisting of four segments. Via choice of        the thickness parameter of the lame it is possible to make an        element consisting of a phase lame for depletion and a neutral        lame for excitation.    -   Gould et al. [45], uses a SLM for creating separately the        lateral and/or axial distributions of depletion. This solution        varies the parameters dynamically for adapting to different        wavelengths. Other works integrate lateral and axial        distributions on a single SLM.

However, the proposed solutions described above are all highly chromaticand are designed for a single excitation and depletion wavelength.However, in many cases biological applications need a system having twoor more excitation wavelengths. In fact, it is current practice to markdifferent biological objects with fluorescent markers differentiated bytheir excitation or emission wavelength. The most highly evolvedfluorescence systems can utilise four to six differentiated markers. Thepresence of a single superresolution path substantially limits use ofthe systems. STED systems having two wavelengths are also availablecommercially.

It is clear that for an achromatic STED microscope or 3D STED microscopewith several wavelengths, use of the same optical path for two depletionbeams having two different wavelengths will simplify superresolution ondifferent fluorophores.

In the prior art for all solutions proposed for STED, the initial laserbeams are in the form of regular distribution and in most cases Gaussiandistribution. These initial laser beams will be later transformed intoan excitation beam, a regular wave, and into a depletion beam, asingular wave, by an adequate optical system, as described by variousinventors. Collocating these beams upstream when they are still in theform of Gaussian distribution is relatively simple. Collocating thesebeams downstream when they have been transformed into a regular andsingular wave is much more complex. Collocating these beams upstream canbe done commercially by laser bank systems using techniques based onfiber optics. It is therefore relatively easy as is also done in allconfocal microscopes to create a set of laser outputs at differentwavelengths of the same fiber optic and therefore collocated highlyprecisely.

The solution proposed in embodiments of the present invention is basedon this upstream collocation, greatly simplifying the system andcarrying out STED at several wavelengths intrinsically. For this, it ispreferable to use an optical system combining the properties of commonoptical path, achromaticity and “beam shaping”. It is preferable toproduce different beam shaping for the different beams, or a regularwave for the excitation beam and a singular wave for the depletion beam,and this at any wavelength in the visible or infrared spectrum. Thecapacity for performing achromatic beam shaping, producing forpolarization a regular wave and for another polarization a singular waveover the entire range of visible or infrared light, different fordifferent polarizations, is novel. The PSIT module creates such anoptical system which combines the properties of common optical path,achromaticity and “beam shaping”. As far as is known there is in fact nosystem in the literature having a path common, which is achromatic andwhich enables beam different shaping for different beams. Such a systemwould definitely improve the simplicity of design and use of STED.

3D STED

Many systems have been proposed to extend the concept of the STED in thethird dimension. The solution used for the set of STED-3D is the“depletion ring” proposed by the Stefan Hell team, reference 36. The“depletion ring” creates a “black sphere”, distribution in which theintensity is zero at the centre of the focus field, and increasesrelatively rapidly with defocusing. Implementation of the “black sphere”has been described by Zhang, [29], creating a black spot enclosed inthree dimensions by a light sphere, and by one of the authors of thispatent in reference 37.

Acronyms

In this patent application we use the acronym, SRCD, “Super Resolutionusing Conical diffraction” to name the platform, modules and systemsspecific to the implementation of this invention.

In this patent application we use the acronym PSIT “Projected Sequenceof Intensities with various topologies” method; the PSIT method can alsobe used to project sequences of light intensities differingtopologically, at two or more wavelengths, sequentially orsimultaneously.

In this patent application we use the acronym, PDOS, “Position DependentOptical Semaphore”.

The SRCDP platform, “Conical diffraction using Super ResolutionPlatform” is a platform for microscopy using optical modules based onconical diffraction.

In this patent application we use the acronym LatSRCS to name theoptical module implementing the PSIT method for the implementation ofthis invention.

In this patent application we use the acronym LongSRCS to name theoptical module implementing the PDOS method.

The SRCDP platform, described in detail hereinbelow, comprises mainlytwo hardware modules, two new and complementary optical modules, theLatSRCS and LongSRCS optical modules, mounted on a microscope, and analgorithmic module SRCDA “Super Resolution using Conical DiffractionAlgorithm”, to reconstruct the information of the superresolved sample.Additionally, the SRCDP platform includes an improved detection module,a control module of the system, and software support.

In addition, certain embodiments of the invention relate to a largenumber of variants of implementations of the PSIT and PDOS methods,platform SRCD, LatSRCS and LongSRCS optical modules and SRCDAalgorithmic.

DETAILED DESCRIPTION OF THE INVENTION Light Distributions LightDistributions Created by Conical Diffraction

Referring to FIG. 7 a, this figure shows the light distribution, createdthrough a conical crystal with a normalized conical parameter ρ₀ of0.388, calculated by a scalar approximation for different input andoutput polarization states, including at input or output either acircular or linear polarizer or a radial or azimuthal polarizer. Theselight distributions were calculated in an imaging intermediate plane andnot at the focus of the objective to separate the conical refractionfrom vectorial effects. The input and output states of polarization arecharacterized by their angle for linear polarizations and theirchirality for circular polarizations.

Referring to FIG. 7 b, this figure shows the light distribution, createdthrough a conical crystal with a normalized conical parameter ρ₀ of0.818, calculated by a scalar approximation for different input andoutput polarization states, including at input or output either acircular or linear polarizer or a radial or azimuthal polarizer. Theselight distributions were calculated in an imaging intermediate plane andnot at the focus of the objective to separate the conical refractionfrom vectorial effects. The input and output states of polarization arecharacterized by their angle for linear polarizations and theirchirality for circular polarizations.

These figures present a large number of different transfer functions,including the case including at input or output circular, linear,azimuthal or radial polarizers. This description has to be completed byincluding circular, linear, azimuthal or radial polarizers described inthe figures, the case of elliptical, dichroic or partially dichroicpolarizers, and polarizers varying spatially. Also, as illustrated inFIGS. 7a and 7 b, these transfer functions vary considerably as afunction of the standardised conical parameter ρ₀. Also, theintroduction of two conical crystals, or one conical crystal and oneuniaxial or biaxial crystal (in which light propagates in one directionof propagation different to that of conical diffraction) in cascadeallows an even greater number of transfer functions as illustrated fortwo conical crystals in FIG. 7 c.

In summary, in this patent application we reference under the term ofconical diffraction transfer function the set of transfer functionswhich can be obtained by means of a low (<6) number of crystals incascade, and polarization elements, static or dynamic, uniform orvarying spatially.

We denote mainly the following light distributions:

-   -   The fundamental, FIG. 7a ₀₀ and FIG. 7a ₁₁ obtained between        parallel circular polarizers, which is a distribution close to        the Airy distribution    -   The vortex: FIGS. 7a ₀₁ and 7 a ₁₀ obtained between crossed        circular polarizers    -   The distribution that we called the “crescent moon” distribution        or Stokes; subfigures 7 a _(0,2-5), 7 a _(1,2-5), 7 a _(2-5,0)        and 7 a _(2-5,1), and FIG. 7c describing the axial variation in        distributions by “crescent moon” or Stokes. These distributions        are obtained between a circular polarizer and a linear polarizer        with a variable angle; this distribution is antisymmetric and        the axis rotates following the linear polarizer axis.    -   The distribution that we called the “half-moons” distribution;        subfigures FIGS. 7a ₄₂, 7 a ₃₅, 7 a ₂₄ and 7 a ₅₃, is obtained        between two crossed polarizers; this distribution is symmetric.    -   The distribution called “offset half-moons” distribution, FIG. 7        d, showing “offset half-moons” distribution at different axial        positions, is obtained between two elliptical polarizers for        some ellipticity values.    -   In reference to FIG. 7 e, this invention describes a novel        distribution, the distribution called “Dark Helix”, created by        positioning a half-wave plate between two equal crystals of        conical diffraction. The particular feature of this distribution        is that it can be performed either with circular input        polarization and without analyser, or without input polarizer        and with a circular analyser. This property simplifies the        optical system and reduces photon loss inherent in many systems        based on polarization.    -   The more complex light distributions, FIG. 7 b, for a crystal        with a normalized conical parameter, ρ₀, greater than 0.5.    -   The creation of additional light distributions using two—or        more—crystal cascading conical crystals (not shown) with or        without static or dynamic polarizing elements between the        crystals.

The different light distributions are carried out by modification of theinput or output polarization. The different light distributions followthe same optical path and the optical system creating thesedistributions is an optical system of common path, such as definedpreviously. There is a number of polarization elements having differentpolarization at different wavelengths. The use of one of these elementscreates two waves compact, either regular or singular at two wavelengthsor a regular wave at one wavelength and a singular wave at anotherwavelength. Such a device enables far simpler implementation ofemission-depletion concepts limited in some cases by tolerances or byvibrations of the optical system.

The above description, although valid for any optical beam, mainlydescribes for the optical LatSRCS Module, described later, the formingof an excitation beam or a depletion beam.

Yet, conical diffraction can be used for forming the emission beam, asfor example in the LongSRCS module, described later. A novel variant ofthis module consists of forming the PSF such that it presents lateraland mainly axial variations. This modification of the PSF of theemission beam, referenced as “PSF” has many applications in differentdisciplines. For example, a module based on conical diffractionmodifying the PSF to create axial dependence can enable measuring oflongitudinal and lateral position of one or more nanoemitters, asdescribed hereinbelow.

Redundancy and Random Phase Variations

The elementary light distributions described in FIG. 7 can be obtainedin several ways. In addition, some of them can be obtained as a linearcombination of other elementary light distributions, e.g. the vortex canbe obtained by the sum of any two orthogonal “half-moons” lightdistributions.

This redundancy allows some averaging of random phase errors inevitablypresent in many measurement process of biological objects.

New light distributions can also be obtained as mathematicalcombinations of elementary light distributions. The “pseudo-vortex”,light distribution, calculated from arithmetic combinations of the fourdistributions “in crescent moon” has the feature of having a strongcurve at the origin.

Vector Effects and Direction of the Fluorescent Dipole

The theory developed so far describes the light distribution in theimaging plane of the microscope, 35. The distribution of the lightprojected on the sample is, according to the theory of the geometricalimaging, a reduced image of the light distribution in the image plane.

However, as described extensively in the literature, for a highnumerical aperture objective, the imaging geometric theory is notaccurate and vector effects must be taken into account. These effectsconsist essentially in the presence of a component, longitudinallypolarized.

Referring again to FIG. 6 a, to mitigate vector effects, it may beadvantageous to maintain the final analyser fixed and to add anadditional element, fixed or variable, the output polarizationadaptation submodule, 74, for controlling the output polarization. Wefound that an output polarization with circular symmetry substantiallyreduces vector effects and can be adapted to the direction offluorescent dipole. Such polarization can be circular, radial orazimuthal or position dependent. For circular polarization, the outputpolarization adaptation submodule, 74, is simply a quarter waveretardation plate. In this case, the elements of longitudinalpolarization have vortex symmetry and integrate harmoniously into thesystem with only a small change in the form of the Stokes parameters,even for microscope objectives with high numerical aperture.

Alternatively, the output polarization adaptation submodule, 74, may bevariable and/or controllable and adapt to the topology and the symmetryof each of the compact light distribution.

*Modified Wollaston Prism

It is recalled that a Wollaston prism can be used for separating anincident beam into two emerging beams separated by an angle. By usingseveral prisms in cascade, an incident beam can be separated into alarge number of emerging beams. The same effect can be obtained bymodifying the Wollaston prism to create the compound Wollaston prism byadding pieces of uniaxial crystal whereof the index and orientation ofthe birefringence are suitably selected. In this way a prism of a singleblock of uniaxial crystal can be constructed which can separate anincident beam into 2^(n) emerging beams (for example eight or sixteen)which are contained in one plane and separated by equal angles. Oncefocused on the sample, the result is 2^(n) points aligned and equallyseparated. If the incident beam has passed through a LatSRC module,these 2^(n) points are not 2^(n) Airy patches, but the distributionscreated by the module are all identical. The advantage of using thisbeam splitter is to scan the sample faster since there are 2^(n) lightpoints in place of a single one.

The modified Wollaston prism can be coupled with methods described inthis invention to duplicate all light distributions without modifyingthe relationships between them.

The modified Wollaston prism can be coupled with STED methods describedin this invention or other standard STED methods to duplicate all lightdistributions without modifying the relationships between them.

Measuring Paradigms

The functionality of the confocal microscope is limiting in threespatial dimensions, the observed region of the sample volume to a sizeas small as possible, volume analysis.

As a corollary, in a confocal fluorescence microscope, the informationretrieved is a single value of intensity for the entire volume analysis,considered as a single entity. More clearly, detailed information on theposition of nanoemitters within the analysis volume is not available, apriori, in a confocal microscope. It was generally agreed that noadditional optical information could be created that would allow furtherdiscrimination within the illuminated volume.

Referring now to FIG. 4 d, which is a simplified conceptualrepresentation of the paradigm of the measurement according to at leastone embodiment of the invention. The paradigm is much more ambitiousthan that of the fluorescence confocal microscope, shown schematicallyin FIG. 4 a. In FIG. 4 d, a test volume, 60 is created at the focalplane of the microscope objective, 22; it contains a sparse object, 51,consisting of several nanoemitters, 53 to 59; the result of the systemis a reconstructed sparse object, 63, and a list of nanoemitters and alist of their attributes, 64.

Reference is now made to FIG. 4e which is a simplified conceptualrepresentation of another measuring paradigm, based on the concepts ofSTED, according to at least one embodiment of the invention. In two(STED 2D) or in the three spatial dimensions, (STED 3D), this measuringparadigm limits the observed region of the sample at the smallestpossible volume of size, the analysis volume. In FIG. 4e an analysisvolume, 60, is created at the focal plane of the lens of the microscope,and contains a sparse object, 51, comprising several nanoemitters, 53 to59; via an depletion effect, one or more depletion waves, 2000, reducethe analysis volume to a lesser volume represented by 2001. In thisparadigm, as in the confocal, superposition of all the effects creates asmall volume, the analysis volume, 60. This volume determines the sizeof the elementary region detected by the system.

Reference is now made to FIG. 4f which is a simplified conceptualrepresentation of a third measuring paradigm, combining the two previousparadigms and used according to at least one embodiment of theinvention. In FIG. 4f an analysis volume, 60, is created at the focalplane of the lens of the microscope and contains a sparse object, 51,comprising several nanoemitters, 53 to 59; via a depletion effect, oneor more depletion waves, 2000, reduce the analysis volume to a lesservolume represented by 2001. As in FIG. 4 d, this volume contains asparse object, 51, consisting of several nanoemitters, 53 to 59; but incontrast to FIG. 4d and similarly to FIG. 4 e, the elementary volume isreduced by one or more depletion waves. The result of the system is areconstructed sparse object, 63, and a list of nanoemitters and a listof their attributes, 64. The use of a sparse object in FIGS. 4d-f is forillustration and this figure would have been perfectly able to representa continuous object, mutatis mutandis.

Measuring Methods PSIT Measuring Method

A method of measurement PSIT according to one embodiment of theinvention, projects a sequence of light distributions of differenttopologies, on the analysis volume.

The measurement PSIT method, performs the following functions:

-   -   Projection of a sequence, the emission sequence of compact light        distributions of different topological families on a sample; and    -   For each compact light distribution:        -   emission of light by nanoemitters on the sample,        -   creation, by means of the microscope optics, of an optical            image,        -   acquisition of the optical image on a photodetector and            creation of a digital image.

In more detail, it is noted that:

The transmission sequence comprises at least two point like lightdistributions, of different topological families.

The transmission sequence is projected onto a biological sample labelledwith nanoemitter. The light emitted, emerging from each nanoemitter, isdependent for each nanoemitter of the light intensity, in the incoherentcase or on the electromagnetic field, in the coherent case, incident onthe three-dimensional spatial position of the light nanoemitter, theaforesaid light sampling property of the nanoemitter discussedpreviously.

For each light distribution pattern of the transmission sequenceprojected on the sample, an optical image is created. The set of imagescorresponding to all the light distributions of the transmissionsequence is referred to as the sequence of images.

The PSIT method according to this embodiment can acquire mainly lateralinformation, i.e., the lateral position of each of the nanoemitters.

In an embodiment, the PSIT method is implemented by the projection oflight distributions of different topologies created by conicaldiffraction and modified by a variation of the polarization states ofinput and output.

In an embodiment, the PSIT method can also be used to project sequencesof light intensities differing topologically, at two or morewavelengths, sequentially or simultaneously.

PSIT Method and Axial Superresolution

PSIT method was originally designed to allow lateral superresolution,however PSIT method can also be used to obtain the longitudinal positionof a nanoemitter. Indeed, some elementary light distributions arerelatively insensitive—within reasonable limits—to a variation of thelongitudinal position of the nanoemitter, others are rather sensitive. Asequence of compact light distributions, some of them independent andsome of them depend on the longitudinal position would reveal thelongitudinal position of nanoemitters.

In addition for the light distributions which are highly dependent onthe longitudinal position of the nanoemitter, a series of elementarylight distributions slightly shifted longitudinally, one relative to theother can be projected on the sample, allowing a set of imagescontaining longitudinal information.

Original PDOS Method

The PDOS method according to an embodiment of the invention includes thedistribution of an “optical semaphore” of the light re-emitted by thenanoemitters between at least two detectors. It has been described byone of the inventors, [37].

Ideally, the function of the optical semaphore is to separate differentareas of the test volume on different detectors. Practically, theoptical semaphore creates, for each detector, a transfer function of thelight emitted by a light nanoemitter, depending on the position in spaceof the light nanoemitter and different for the different detectors.

In an embodiment, the PDOS method is implemented to separate ondifferent detectors the collimated light, emerging from nanoemitterspositioned at the focal plane of the objective lens, from non-collimatedlight emerging from nanoemitters lying within or beyond the focal plane.

The PDOS method, allows acquiring essentially longitudinal information,i.e., the longitudinal position of each of the nanoemitters.Mathematically, the method according to some embodiments of theinvention provides a transfer function converting the spatialdistribution of the nanoemitters in space in unprocessed informationconsisting of a set of images. The algorithmic performs the inverseoperation: it reconstructs the spatial distribution of the nanoemittersin space from the set of images in the raw information.

Modified PDOS Method

The modified PDOS method is also presented, an optical method forforming the emission beam for the axial and/or lateral location ofnanoemitters. This method implements a PDOS method on a single channelin which the variation of one of the parameters describing thedistribution created is used for measuring axial or lateral parameters.The parameters used can be either a parameter of angle for adistribution having axial helicoidal variation, or the ratio between thelobes of the distribution—for a distribution having two lobes (or more)having axial variation. This method has a certain similarity with theoriginal PDOS method described by one of the inventors in [37], butdiffers by the variation of the topology of the distribution createdbeing used to measure the axial or lateral parameters and not by anintensity ratio between two detectors, as described in the originalversion of the PDOS method. This method, as for the original method, hasapplications as complementary method of the PSIT method, but also forthe axial location of nanoemitters, for example for location modalities,such as for example PALM, STORM or GSDIM modalities or similar.

PDOS Method and Lateral Measurements

Method PDOS was originally designed to allow longitudinalsuperresolution, however PDOS method can also be used for measuring thelateral position of a nanoemitter. Indeed, the elementary lightdistributions are also sensitive to variation of the lateral position ofthe nanoemitter. For a plane sample, in the case where the lightprojection is not possible, the method PDOS may replace the PSIT methodfor performing superresolution measurements.

All these variants are considered part of the invention. The inventorhas yet chosen in one of the implementations to separate into twodisjoint, separated, but complementary optical modules the lateralmeasures from the longitudinal measures to reduce the complexity of eachone of the complementary modules.

Information in Certain Embodiments of the Invention

In certain embodiments of the invention, the intermediate result, theraw information is obtained at the end of the detection step. Rawinformation comprises a set of images A_(op)(m,n) representing for the olight distribution, the image from the detection channel p.

As in a confocal microscope, the measurement process analyses a smallvolume in a much larger object. It will therefore require the additionof additional modules, similar to those of a confocal microscopeincluding a scanning process, a software module integration, analysisand visualization of data points in surfaces and/or three-dimensionalobjects.

In mathematical terms the algorithm solves an inverse problem orparameter estimation. The model equations are known and a model,parametric or not, is used a priori on the configuration ofnanoemitters. The most natural model consists of supposing a low numberof nanoemitters (sparse object), but continuous models can also be used,supposing the presence of unidimensional structures (lines, curves) orspecific patterns. So we can use all the mathematical procedures knownto those skilled in the art for solving inverse problems and parameterestimation. We describe later an example of algorithm adaptedspecifically to the measurement according to an embodiment of theinvention.

In addition, we present, for its symbolic value, a new solution to theproblem of discrimination of two points located at a small distance fromeach other. This problem studied by Lord Rayleigh, is the base of theresolution criterion in many areas of Optics.

It has thus been described, rather broadly, the characteristics of theembodiments of the invention in order that the detailed descriptionthereof may be better understood, and in order that the presentcontribution to the art may be better appreciated. Many additionalfeatures of the invention will be described below.

System Hardware and Algorithmic Platform

A method according to one embodiment of the invention is a hardware andalgorithmic platform, referred to as the SRCDP platform, 500, shown inFIG. 5.

The SRCDP platform, 500, implements the method according to anembodiment of the invention, either by combining the two PSIT and PDOSmethods, original or modified, described hereinabove, or by using STEDtechniques, or by combining STED techniques with PSIT or PDOS methods,original or modified.

In one of the embodiments, the SRCDP platform observes, FIG. 5, abiological sample, 11, including a plurality of nanoemitters. The resultof the observation of the biological sample by the SRCDP platform is theacquisition of superresolution information, representative of theobserved sample.

The SRCDP platform, 500, FIG. 5 includes mainly:

In its hardware part:

-   -   A confocal microscope 200, adapted or optimised, similar to the        confocal microscope, described previously, and including all        appropriate components, as previously described    -   Two new and complementary optical modules, mounted on a standard        microscope. The two new optical modules are LatSRCS, 700, and        LongSRCS, 800, optical modules described in detail later with        reference to FIGS. 6 and 8, respectively. The LatSRCS optical        module 700, implements the steps of illumination required for        implementing the PSIT method according to one embodiment of the        invention. Alternatively, the optical LatSRCS module 700        implements the illumination steps necessary for implementation        of a STED or RELSOFT technique according to another embodiment        of the invention. The original or modified, optical LongSRCS        module, 800, implements the steps of the light intensity        distribution in a plurality of emerging images of the PDOS        method or implements the variation of the emerging PSF as a        function of lateral or axial parameters, according to an        embodiment of the invention, and    -   SRCDA algorithmic module, 600, is able to reconstruct        superresolution information of the biological sample from images        created by the SRCDP platform.    -   Other auxiliary elements, such as computer 66 and software 67,        can be necessary for the realization of the platform,

Detection Module

In scanning confocal microscopy, the detector is a detector consistingof a single element as a PMT or SPAD. The acquisition time of thedetector is determined by the scanning mechanism.

An improved detection module, 65, may be implemented using smalldetectors with low number of pixels. Such a module would not have beenpossible ten or twenty years ago, due to the lack of appropriatetechnologies. Today, small detectors with small number of pixels, athigh speed, with low noise characteristics are available on the basis ofseveral technologies. SPAD arrays with a small number of pixels, such as32*32 have been shown recently with acquisition rates up to 1 MHz. Theimproved detector module 65, may also be implemented using CCD, EMCCD orCMOS sensors. CCD sensors, CMOS and EMCCD with a small number of pixelsexist or can be specifically designed. In addition, CCD sensors, CMOSEMCCD can be used using features as region of interest, sub-windowing or“binning”, “crop” or “fast kinetics” modes, available for somedetectors.

The space-time information referenced herein is the position and thetime of the impact of each fluorescent photon. In real systems, thespace-time information is corrupted by the noise of the detector, whichcreates incorrect photons, and by inefficient detection, creatingphotons which are not detected, thereby reducing performance. In SPADarrays, for each photon, the pixel that has detected it and the time ofimpact are received, i.e. the full spatiotemporal information isavailable. For CCD sensors, CMOS or EMCCD, the acquisition of multipleframes is necessary to approximate the space-time information.

In several implementations we will refer to separate detectors; in manycases the sensor can be either physically separated or consisting ofdifferent areas on a single detector, or a combination of the twoprevious cases.

Control Module

With reference to FIG. 11 and FIG. 5, in one preferred embodiment ofthis invention, the various control elements integrated into the SRCDPplatform, 500 will be described:

The control module, 1100, using the procedure of systemic control, 1101,monitors and modifies the optical parameters of the SRCDP platform, 500,the electronic parameters of the improved detection module, 65, and themathematical parameters of algorithmic procedures SRCDA, 900, tooptimise the emerging information in accordance with criteria defined bythe system or by the user. Control is achieved by varying controlsystems 1102, 1103 and 1104, of the various elements of the platform,600, 800 and 900. The control system 1100, also use, if available,external information, 1105, relayed by computer support. Remark: 1105 isnot present in FIG. 11.

It is understood that the invention is not limited in its application tothe details specified in the description contained here or illustratedin the drawings. The invention is capable of other embodiments and beingpractised and carried out in various ways. Those skilled in the art willeasily understand that various modifications and changes can be appliedto the embodiments of the invention such as described previously withoutdeparting from the scope of this invention.

SRCDA Algorithmic

The reconstruction algorithm detailed above applies not only in the caseof a given field analyzed by means of PSIT and PDOS methods, but also inthe event where the measurements obtained by the PSIT and PDOS methodsare enriched by additional measurements, using other Microscopymodalities. For example, measurements in confocal microscopy orwide-field, at the same lateral or axial positions, or at differentpositions can be taken for setting certain parameters of the model ofthe scene. In the case of confocal microscopy, the direct model isenriched by the fact that coverage between the different positions ofsignals projected takes into account, at a given point, moremeasurements. But considering offset projected signals brings noadditional complexity, since these offset signals only add to the listof projected signals.

Reference is now made to FIG. 9 which is a simplified schematicillustration 900 of an algorithm method for superresolution offluorophore data, according to an embodiment of the present invention.

An algorithm procedure presented in FIG. 9 quantifies the number offluorophores, retrieves the attributes of each fluorophore andquantifies the precision of each output parameter.

The pre-processing procedure, 111, reorganises the space-timeinformation, 110, in sets of superresolution images, 112. This operationcan be done by using a filter bank procedure. The intermediate set ofdata is a short series of small images, typically 16*16 pixels. Thepre-processing procedure applies to a small number of space-timeelements of the order of a few thousands, and can be executed in realtime and using existing computer equipment.

The descriptor procedure, 113, the main calculation step, creates fromeach image a set of descriptors, 114, and their statistical pertinence.The descriptors comprise, but are not limited to: the intensity of eachimage, the presence on the image of distribution of light and itscharacterisation as regular distribution or a vortex, its centre ofgravity and its moments of order one and more.

The third step is a filtering operation, 115, in which only thedescriptors, which are statistically pertinent, are retained.

The classification operation, 116, is the final step of the algorithm.On the basis of the set of descriptors, 114, and a basis of knowledge,117, the algorithm is capable of recognising the different measuringcases as a single fluorophore, two fluorophores separated longitudinallyor laterally and three or more fluorophores.

The SRCDA algorithmic can utilise classic techniques of inverseproblems. But three novel optical approaches, the modified MAPalgorithm, the E-LSE algorithm and the ICE algorithm are described inthis patent application and form part of this invention.

Optical Modules LatSRCS Optical Module Implementing the PSIT Method

We describe, with reference to FIG. 6 a, an optical module according toan embodiment of the invention, the LatSRCS optical module, 700, and itsspecific function in microscopy.

The LatSRCS optical module, 700, according to this embodiment is anoptical module, projecting on a plurality of nanoemitters in a sample, asequence of compact light distributions of different topology. Eachnanoemitter fluoresces with a sequence of fluorescent light intensitiesdependent on the incident intensity on the nanoemitter andcharacterizing the lateral position of the nanoemitter. In mostembodiments, the light compact distributions of different topologies arecreated by interference with variable amplitudes and phases between anordinary wave and singular wave. In the preferred embodiment, theregular and singular waves are created by a thin conical crystal.

The LatSRCS optical module, 700, is positioned in the illumination pathof the confocal microscope 200; it projects a sequence of compact lightdistributions of different topologies on the sample 11 using theconfocal microscope objective 200. In the embodiment using the conicaldiffraction, the incident intensity at a specific position on the sample11 will be proportional for each light distribution pattern, to aspecific combination of the Stokes parameters.

The LatSRCS optical module, 700, uses an inherent feature describedabove, specific to the nanoemitter, which samples the intensity of lightincident on its precise position (the nanoemitter), and re-emitsfluorescent light dependent on the incident light. It is remarkable thatthe measured information is directly related to the position of thenanoemitter in the compact light distribution. This information isfrozen by the functionality of the fluorophore, its ability to absorband re-emit light, breaking the optical chain. This information iscarried by the fluorescent light as an emerging light distributionrecoverable by a detector assembly 65.

If the incident light varies temporally according to a sequence ofcompact light distributions of different topologies, the intensity ofthe fluorescent light re-emitted varies in the same proportions. Thesequence of the re-emitted fluorescent light is proportional to thesequence of compact light distributions of different topologies. Fromthis information, it is possible to retrieve the position of thenanoemitter, as explained below.

The PSIT method, according to embodiments of the invention, refers tothe projection of a sequence of compact light distributions of differenttopologies in a microscope, the interaction with the sparse object andthe continuous object, collecting the reflected light by the objectiveof microscope, 22, detecting the fluorescent light or not, by theimproved detector assembly 65, and the analysis of the information by asuitable algorithm. In some embodiments, the improved detectionassembly, 65, comprises a single detector, and recovers only the overallintensity as a function of time, while in other embodiments the improveddetection assembly includes a small area of pixels and recovers also thespatial distribution of the fluorescent light. All retrieved informationconsisting of a plurality of images, the named as lateralsuperresolution images.

In one of the embodiments, the contribution of a nanoemitter in theilluminated volume positioned in a specific lateral superresolutionimage is proportional to a specific combination of the Stokes parametersof the incident light at the nanoemitter position.

This new information helps to refine the position of the nanoemitters orthe spatial distribution of the continuous object, to quantify thenumber of nanoemitters present in the illuminated volume and todifferentiate multiple nanoemitters present in the same volume.

We refer now to FIG. 6 a, which is a simplified schematic illustrationof a LatSRCS optical module, 700 in accordance with an embodiment of thepresent invention.

FIG. 6a shows a LatSRCS optical module, 700; it includes all thecomponents of the module of conical diffraction, of FIG. 3, which areimplemented in the same way as in the module 300 of conical diffraction.The optics of the light source of the scanning confocal microscope isassumed to be achromatic and infinite conjugate, although otherconditions can be adapted using auxiliary optics. The incident lightentering from the light source is parallel, 30. The optical moduleitself, 700, comprises a first lens 31, an achromatic 32, or a subsetachromatically performing the functionality of a conical crystal asexplained previously, and a second lens 33; a partial polarizer, 29,described above, may also be added. The first two lenses 31 and 33 arepreferably configured in the form of a Kepler telescope of ratio of 1:1;the conical imaging plane, 35, is placed in the common focal plane ofthe objective lenses 31 and 33. The numerical aperture of the firstlens, 31, determines the parameters of the conical diffraction effectthrough the conical normalized radius, defined below. The secondobjective 33, restores the parallelism of the light, to inject it in themicroscope. It further comprises a sub-module of polarization control71, including, for example, a rotating quarter-wave plate, a pair ofliquid crystal light valves or a Pockels cell, 72 and an analyser 73.The information of the Stokes parameters can be converted into sequenceinformation, through a sequence of light distributions spatiallydifferentiated and carrying sequential information, as described above.

Modified LongSRCS Optical Module for Forming the Emission Beam

The modified LongSRCS module is also presented, an optical module forforming the emission beam, for axial and/or lateral location ofnanoemitters. This module implements a PDOS method on a single channel,in which variation of one of the parameters describing the distributioncreated is used for measuring the axial or lateral parameters. Theparameters used can be either a parameter of angle for distribution ofhelicoidal axial variation, or the ratio between the lobes of thedistribution—for distribution of two lobes (or more) of axial variation.This module has a certain similarity with the original LongSRCS module,described by one of the inventors in [37], but differs in that thevariation in topology of the created distribution is used to measure theaxial or lateral parameters and not by an intensity ratio between twodetectors, as described in the original version of the LongSRCS module,[37]. This module, as for the original module, has applications such ascomplementary module of the LatSRCS module, but also for the axiallocation of nanoemitters, for example for location modalities, such asfor example the PALM, STORM or GSDIM modalities or similar.

The case where the input polarization and the output polarization areelliptical with orientation of the big axes of each ellipse having anangle of 90° between them is treated in more detail. Of distributionsgenerated in these conditions some show substantial axial variations,and these variations can be exploited to measure the position of anemitter with considerable axial precision.

These distributions are separated into two groups, distributions whichhave a single lobe and those having two lobes. Distributions with asingle lobe have a rotation effect along the axis Z. In this way, Stokesdistributions, created from linear polarization (ellipticity=0°) andcircular polarization (ellipticity=45°) show variations which appear inthe table below. By using an appropriate algorithm the orientation ofdistribution can be detected and the position of the emitter deducedwith considerable axial precision. (FIG. 7c ).

In addition, some more complex elementary light distribution, consistingof more complex overlapping of waves with a strong longitudinaldependence exist, e.g. the “three-dimensional dark spot” described byZhang, [29], which create a black spot surrounded in three dimensions bya luminous sphere. These “three dimensional obscure spots” consist of asuperposition of Laguerre-Gauss functions, which can be achieved withina laser cavity or using a hologram or a phase plate, as suggested byZhang, or using uniaxial or conical crystals as suggested by theinventor in [37].

3D Localisation

Certain distributions with two lobes or more have an offset effect ofboth lobes according to the axis Z. So, distributions called offsethalf-moons created from two elliptical polarizations oriented at 90° butwith the same ellipticity have variations. By using an appropriatealgorithm, the position of the emitter can be deduced with considerableaxial precision by measuring the intensity ratio between the lobes, thisvariation being illustrated in FIG. 7 d. This 3D location can be usedeither in projection, i.e., by projecting one or more distributions withoffset half-moons onto the object and by using an adapted algorithm, forexample the algorithms described in this invention, or in emission byhaving the light emitted pass through an optical module creating thisdistribution and by analysing the return PSF.

The “dark helix” distribution presents a rotation effect of the axisconnecting the two zeros according to the axis Z. Using an appropriatealgorithm the position of the emitter can be deduced with major axialprecision by measuring the axis connecting the two zeros. This 3Dlocation can be used either in projection, i.e., by projecting one ormore distributions with offset half-moons onto the object and by usingan adapted algorithm, for example the algorithms described in thisinvention, or in emission by having the light emitted pass through anoptical module creating this distribution and by analysing the returnPSF.

Spherical Aberration

In terms of optical fluorescence microscopy, or any optical system inwhich the illumination of the sample is uncoupled from the imaging ofthe sample, an invention is proposed which evaluates the sphericalaberration locally in each place of the sample, or each place of theobject being imaged.

It is known that the illumination beam can be formed by using conicaldiffraction and its phase and polarization effects. The sample isilluminated with uneven light distribution, which can also be a blacksphere (or top hat) such that 3D distribution presents two lobes of thesame intensity below and above the focal plane. In the presence ofspherical aberration in the system these two lobes do not have the sameintensity. This effect can be used to take an image, a confocal image inparticular, by illuminating above and below the focal plane (byuncoupling the illumination and imaging). Analysing the intensity ratioof the two images then gives the quantity of spherical aberration of thesystem.

Another approach for measuring the spherical aberration uses anothervariant of systems based on conical diffraction.

Determination A Priori and Measuring of the Spherical Aberration

Forming a light beam by conical diffraction via a cascade of crystalsobtains a distribution of intensity connected directly to sphericalaberration.

This distribution is obtained between crossed linear polarizers and twobiaxial crystals whereof the optical axes are aligned. A half-wave plateis inserted in between the two crystals. By way of characteristic form,this distribution will be called “four-leafed clover”. In the absence ofspherical aberration, this distribution comprises four perfectly equallobes and a1 in the same focus.

Reference is made to FIG. 12 which describes the rupture of symmetrycreated in a “Four-leaf-clover” distribution in the presence ofspherical aberration. FIG. 12 shows the simulated distributions underMatlab for different values of defocus and spherical aberration. Thespherical aberration caused by an optical system breaks the symmetry ofthis distribution at the same time in the focus and the distribution ofintensity in the four lobes as is evident in the figures below showingthe “Four-leaf-clover” distribution of different values of sphericalaberration. Simple qualitative observation allows a binarypresence/absence test of spherical aberration. Fine measuring of thevalue of spherical aberration is possible by a focus-offset estimator oflobes and ratios of intensity at different focus planes.

Calibration in Real Time of a Beam Scanning System by Point MonitoringGenerated by a Laser Diode in Near Infrared

The optical system described in this invention can incorporate a modulefor tracking in real time on a camera a point scanned by a beam scanningsystem (galvanometric mirrors, bidirectional piezo-electric mirror orany other system). Using a wavelength in the near infrared dispenseswith chromatic effects of optics which makes this system useable forcalibrating several wavelengths projected in a confocal microscope.Also, using a laser diode in the near infrared ensures that low passageof the calibrating laser in the microscope will have a highly marginaleffect only, the wavelength being far greater than the usual excitationwavelengths of fluorescence.

All these variants are considered part of the invention. The inventorhas yet chosen in certain implementations to separate in two opticalmodules, disjoint but complementary, lateral measurement andlongitudinal measurement to reduce the complexity of each of thecomplementary modules.

SRCDA Algorithm Multi-Image System Including the E-LSE ReconstructionAlgorithms

The name multi-image system refers to all optical and optoelectronicsystems, in which a set of different and differentiated images, comingfrom the same spatial region of the object, bidimensional orthree-dimensional—is registered and analysed via an adequate algorithmfor analysing spatial—and/or spectral—distribution of the emittingspatial region. This differentiation can be due to the projection ofspatially different illumination, such as described previously; it canalso be due to variation in the spectral content of the illumination; itcan also be due to natural movement or imposed from the exterior of theobjects. Finally, it can be due to stochastic variation in the contentof the spatial region of the object, bidimensional or three-dimensional,via a natural or imposed stochastic effect, such as systems used insuperresolution based on stochastic detection, including the PALM andSTORM process and their many variants, each bearing a different acronym.

Other means for differentiation of images of the same emitting spatialregion are known to those skilled in the art and are deemed an integralpart of this invention.

The name multi-image system including the E-LSE reconstruction algorithmrefers to a multi-image system using the E-LSE algorithm describedbelow.

Modified Reconstruction Algorithm MAP

This algorithm differs from existing algorithms in the literature knownto those skilled in the art by presenting the following mathematiccharacteristics the combination of which is novel and differs fromtraditional MAP approaches:

-   -   Bayesian formulation    -   no a priori on reconstruction, aside from positivity (in        contrast to traditional MAP approaches, which in general        incorporate a regularity a priori on reconstruction of total        variation type, for example)    -   modelling of Poisson noise results in a term of attachment to        data written in the form of a Csiszar divergence (well-known        result)    -   the law a posteriori is exploited by a MAP, i.e., the aim is        reconstruction of probability (a problem of maximal minimisation        of energy must therefore be resolved digitally, done via an        iterative approach of gradient descent type)    -   introduction to the model of a resolution gain factor        (oversampling factor of reconstruction relative to the        resolution of acquired images)    -   imposition of a “good sampling” restriction for reconstruction        (the highest frequencies of the reconstruction spectrum are        forced at 0)    -   introduction of a “pinhole” factor (digital confocal)

E-LSE Reconstruction Algorithm

From images registered by the camera (or cameras) following excitationof the sample by all of the selected illuminations the proposedalgorithm reconstructs a high-resolution image, bidimensional orthree-dimensional, of the sample. This algorithm rests on thecombination of several principles:

-   -   formulation of the reconstruction as a reverse Bayesian problem        which results in definition of distribution a posteriori. This        law a posteriori combines, by way of the Bayes law, the        probabilistic formulation of the noise model (Poisson noise        inherent in the quantic nature of the emission of photons on        which the modelling of other sources of noises is optionally        superposed, especially the reading noise of the camera), as well        as any a priori (positivity, regularity, etc.) on the        distribution of light in the sample;    -   The E-LSE algorithm uses the same Bayesian formulation as the        modified MAP algorithm, described previously, but exploited        differently (more completely) the law a posteriori: in fact, the        average of the law is calculated a posteriori and not its point        of maximal value (which is known for being more adapted for        problems of large dimensions) This approach, envisaged by Besag        in 1984 [30], has recently been used digitally in the case of        image denoising with an a priori of total variation type        [31,32];    -   use of clouds of specific or simple geometry emitters which        favours sparse solutions (samples with limited number of        emitters, or whereof the emitters are concentrated on structures        of small dimension such as curves or surfaces in the        three-dimensional case (in fact the average of the law is        therefore calculated a posteriori with a sparse a priori on the        solution);    -   The fact of using the average of the law a posteriori (and not        its point of maximal value) produces low dependency on the        number of emitters used: it is therefore unnecessary for the        number of emitters used to correspond to the number of        fluorophores effectively activated in the sample;    -   estimation of the average a posteriori by means of an algorithm        of Monte-Carlo Markov Chain type (MCMC) [33,34], as in        references [31,32] mentioned above.

According to an embodiment of the algorithm, the sparse a priori by useof a restricted number of emitters is not used and the average of thedistribution a posteriori is calculated on all of the possible images asin [31,32].

Poisson Noise

In the standard embodiment, where only the Poisson noise is modelled,the density of the law of probability a posteriori is written as

$\begin{matrix}{{p\left( {x,\lambda} \right)} = {\frac{1}{Z}e^{- {E{({x,\lambda})}}}}} & \left( {{EQ}.\mspace{14mu} 9} \right)\end{matrix}$

where Z is a standardisation constant—and not the axis of propagation oflight—which does not occur in the algorithm, and

$\begin{matrix}{{E\left( {x,\lambda} \right)} = {\sum\limits_{i,y}\left\{ {{\sum\limits_{k}{\lambda_{k}{u_{i}\left( {x_{k},y} \right)}}} - {{m_{i}(y)}{\log \left( {B + {\sum\limits_{k}{\lambda_{k}{u_{i}\left( {x_{k},y} \right)}}}} \right)}}} \right\}}} & \left( {{EQ}.\mspace{14mu} 10} \right)\end{matrix}$

The cloud of emitters is represented here by the vectors x=(x₁, x₂, . .. x_(n)) (n discrete positions in the field of the high-resolution imageto be reconstructed) and the vector λ=(λ₁, λ₂, . . . λ_(n)) which codesthe intensities of the emitters located at points x₁,x₂, . . . x_(n).Each quantity of type u_(i)(x,y) is determined during the calibrationstep: it represents the intensity sent to the pixel y of the camera byan emitter located at the pixel x of the image high-resolution inresponse to index illumination i (i therefore codes here both theposition of the illumination signal and also its form). The realpositive B corresponds to the intensity of the continuous background,resulting in general at the same time in the sample (diffusefluorescence for example) and also the sensor. Finally, the quantitiesm_(i)(y) correspond simply to measurements (images recorded by thecamera): m_(i)(y) is the intensity measured at the pixel y of the indeximage i, i.e., the image recorded after index illumination i).

The algorithm proposed consists of having the emitters represented byvectors x and λ evolve in accordance with the law given by the densityp(x,λ). The algorithm is iterative: at each iteration one of theemitters is perturbed (in position or intensity) and this perturbationis accepted or not according to the principle of the Metropolis-Hastingsalgorithm [3]. The reconstructed image is obtained by averaging, withequal weight for each iteration, the emitters now constructed. If x^(j)and λ^(j) correspond respectively to the position and intensity of theemitters at iteration j of the algorithm then the image I reconstructedafter N iterations is given by

$\begin{matrix}{{I(x)} = {\frac{1}{N}{\sum\limits_{j,{k;x_{k}^{j}}}\lambda_{k}^{j}}}} & \left( {{EQ}.\mspace{14mu} 11} \right)\end{matrix}$

Several improvements can be made to this algorithm: the introduction ofa burn-in step (the first iterations are not used in thereconstruction), optimisation of the initialisation of emitters,optimisation of perturbations made at each iteration (law ofproposition), the use of a post-filtering step (for example lightGaussian blur), etc.

The results of the algorithm can be transmitted to the user either inthe form of an image or in the form of digital or graphic data.

The same reconstruction algorithm can be used in a second versionincluding a set of additional parameters describing global parameters ofspatial region of the object either known a priori or determined aposteriori.

This algorithm, in its two versions, can be used in all of themulti-image systems, in which a set of different and differentiatedimages, originating from the spatial same region of the object,bidimensional or three-dimensional, are recorded and analysed.

Dynamic E-LSE Algorithm

Also, in a variant of this algorithm, the dynamic E-LSE algorithm, thespeed of emitters can be considered.

During observation of dynamic samples it is possible to simplyincorporate into the E-LSE algorithm the speed of objects observed,either individually for each of the emitters or by defining populationsof emitters having different speeds. In the case of imaging known as“time lapse” (i.e., successive observations over time of the samesample), this can be done naturally by forcing the simultaneousreconstruction of successive images from mobile emitters parameterizedby their initial position and their speed. In the case of acquisition ofa single image it is also possible to consider the dynamic character ofthe scene via its impact on the return PSF (movement blur), whereof thedeformation is correlated with the multiple observation of the sameemitter. The coverage, “overlap” of the different micro-images obtainedduring the scan ensures that the same emitter is solicited duringacquisition of several micro-images (at different instants due to thetime component of the scanning).

ICE Algorithm

The ICE algorithm has recently been introduced for denoising images inthe case of regularization by total variation [39]. The ICE algorithmcan also be used to resolve more complex inverse problems (deblurring,interpolation). This algorithm of fixed point type converges veryrapidly and the resulting solution is extremely close to that associatedwith the LSE algorithm for this problem. The principle of the ICEalgorithm is to replace calculation of the expectancy of the law aposteriori effected by LSE via iteration of the explicit calculation ofthe average of the law a posteriori of a pixel conditionally to itsneighbours. However, application of the ICE algorithm to inverseproblems for an image or for a multi-image system must be shown.

Calibration

In many case, SRCDA algorithms use as input measurements taken on thesample, but also data inherent to the system, which are based either ontheoretical values or on values obtained after a step known ascalibration. In this step, measurements are taken on a reference sampleto precisely measure the functions of illumination and the function ofreturn Transfer (PSF) of the optical system.

Specificities and Advantages of Different SRCDA Algorithms

Different SRCDA algorithms, described previously, present the followingdifferentiations and advantages relative to the prior art:

Modified MAP

production of images naturally well sampled due to introduction ofresolution gain and forcing at 0 of highest frequencies (limitsartefacts of “night sky” type)

good compromise between controlled optical complexity (which keepsacceptable calculation times) and good quality of reconstruction(resolution of the inverse problem by non-linear optimisation, moreinteresting than using linear methods of “reassignment” type, [40] forexample)

E-LSE

-   -   introduction of the sparsity hypothesis in a supple form (low        sensitivity to the number of emitters)    -   reconstructions of very high quality, in particular for sparse        samples    -   capacity of the method to adapt to the quantity of local        information, good management of reconstruction uncertainties        (phenomenon of averaging in case of possible multiple        interpretation)    -   possibility of modelling sparsity differently according to a        priori on the sample observed (use of emitters of point,        segment, curve, surface, type etc., exclusively or in        combination)

Algorithm of the Compound Optical Process

The compound optical process according to at least one embodiment of theinvention is the logical complement of the SRCDA algorithm. Indeed, thereconstruction obtained by the SRCDA algorithm can lead to theconclusion that an additional image would improve performance of themeasurement. The SRCDP microscopy platform allows the acquisition ofone—or more additional images from a set of light distribution of thePSIT or PDOS methods.

Resolution, Sparsity, Topology of Illumination and Positivity

The capacity to exceed the resolution limit for nanoemitters by usingPSIT methods based on the specific topologies of some illuminationscreated by these methods had already been described by one of theinventors in reference [37] and is described again in the nextparagraph.

More generally, a microscopy system using no non-linear effect islimited, in general, to a superresolution factor of 2 relative to thelimit imposed by optical diffraction [38] and [41]. But in the case of asparse scene (real support of the sample substantially less than thesize of the imaged zone, for example in the case of scenes composed offilaments and/or specific sources), and in the absence of an excessivelylarge continuous background (such as a positivity restriction on thereconstructed or efficacious image), it starts to be recognised thatthis limit of 2 is no longer valid and can be exceeded [42-44]. Anevident example is given by the case of observation of a single specificsource, even by using a single image: in this case the resolutionattainable for the reconstructed image (i.e., the precision with whichthe source can be located) is not limited by optical diffraction but bythe quantity of photons (more precisely, by the signal-to-noise ratio ofthe measurement).

In the PSIT method, on the basis of acquisition of several images ofdifferent topologies used in this method, one of the inventors [37] hadshown the capacity of extending this absence of intrinsic resolutionlimit, replaced by a resolution limit linked to the signal-to-noiseratio, in the case of detection of two close points (Rayleigh criterion)and of the measurement of their position. This demonstration can beextended by simple modifications in the case of three points, notpositioned on a straight line. This demonstration is repeated in thenext paragraph. This demonstration is based on a new mechanism formeasuring position, described in the next paragraph, which is differentand complementary to a centroid method used in conventional systems.

In the case of several specific sources, in the case of uniformillumination, apart from the signal-to-noise ratio, the maximalsuperresolution factor depends essentially on properties of the scene:number of sources (relative to the number of measurements), minimaldistance between two sources, etc [43-44]. In the PSIT method themaximal superresolution factor will depend on selected illuminations,apart from the factors described previously.

Detection and Consideration of Light Out of Focus

The following point describes a step of previous or simultaneousanalysis to the use of a reconstruction algorithm for a multi-imagesystem.

The principle is based on exploitation of one of the characteristics ofthe algorithms described previously but not singly, which is that thesignal of interest is located mainly where the excitation light has beenprojected.

It is possible to measure the signal proportion which belongs to theregion of interest (pinhole) for each image i.e., each laser position,each light distribution and each orientation of this light distribution.

This measuring, called Pinhole Ratio, consists of the method asdescribed, of comparing in a spatial region of the object the proportionof photons which are resent and imaged in the region of interest of eachimage coming from this region relative to the total number of photonsresent by the object in all the images considered.

This ratio gives information locally on the nature of the imaged object,if it verifies a predefined model (for example: planar object) in termsof the Pinhole Ratio, or if it deviates sharply from this model.

The criterion defined here can assume values between 0 and 1, and anominal value PR_ref in the event where the object verifies the model.Values lower than PR_ref are associated with an object which does notfully verify or does not at all verify the model as a function of atheoretical or empirical rule.

In the event where the Pinhole Ratio deviates from the aforesaid value,different parameters are applied to the associated reconstructionalgorithm.

It is also possible to use another model and therefore an algorithmother than the initial algorithm, for example by considering additionalmeasurements, which can initially require remeasuring the object withdifferent parameters or light distributions.

It is also possible to change algorithm and add an a priori to theobject to be reconstructed, for example an a priori of regularity asoften found in reconstruction algorithms (standard Ĥ1, sparsity 1̂1, 1̂0,total variation, standards of higher order) to reduce the influence ofobjects outside the model present in the measured field.

Variability of Reconstruction Relative to the Measuring Noise

A step is described here which is prior to or simultaneous with the useof a reconstruction algorithm for a system whereof the measurements arenoised with a noise statistic of Poisson noise type.

A property of the Poisson noise is the possibility of generating fromrealisation of a Poisson VAR of parameter I (average) two independentrealisations of a Poisson VAR of parameter I/2, via processing aposteriori.

Because of a process for generation of random or pseudo-random numbers abinomial law X1 of parameters (n, p) is simulated where n is equal tothe measurement of the initial Poisson variable, and p a separationparameter of photons equal to 0.5 in this case.

X ∼ P(I) X₁ ∼ Bin(X, p)  if  X > 0, X₁ = 0  otherwiseX₂ = X − X₁

Mathematically, this property is a consequence of the formula of totalprobabilities and the entire decomposition in series of the exponentialon R.

At the optical level, this property illustrates the known fact that if aseparator mirror 50/50 is placed in front of the camera which images thefluorescence, and if a second camera for imaging the second fluorescencebeam is placed, in identical imaging conditions the two cameras acquirean average signal equal to half of the initial signal and alwaysfollowing a Poisson law.

Analysis or reconstruction of both measurements generated in this wayand called Split Photon method provides two independent results in termsof probabilities, and the differences between these two resultsillustrate dependence on the reconstruction algorithm relative to themeasuring noise, even though the signal-to-noise ratio is lower in eachmeasurement generated than in the original measurement of a factorsqrt(2).

A local comparison criterion of these two reconstructions is used, herethe local similarity criterion or Local Structural Similarity IndexMethod (LSSIM), but any other local or overall criterion for comparisonof images can be used.

Whenever this criterion is poor in terms of the criterion in question,i.e., there is a significant difference between the two reconstructedimages or signals, different parameters in the reconstruction algorithmapplied to the original measurements are applied.

It is also possible to use another algorithm, such as a MAP algorithmwith overall or local regularity restriction, which uses the similaritymap or any other comparison criterion to optimise the regularizationparameter or the regularization parameters.

It is also possible to take into account the similarity map or thecriterion used in the Split Photon method, graphically or digitally, toillustrate local or overall dependence of reconstruction on themeasuring noise.

It is also possible to generate, rather than a couple of measurements,an n-tuple of measurements, by using rather than a binomial law amultinomial law of parameters (n, p1, p2 . . . pk) where the photonseparation probabilities p1, p2 . . . pk can be different.

Finally, it is possible to iterate the Split Photon method by generatingseveral couples or n-tuples of measurements, still by processing aposteriori of measurements, but by modifying the grain in thepseudo-random generator. In the case of a random generator this producescouples or n-tuples of independent Poisson variables but the couples orn-tuples are not independent of each other. This can reduce falsedetections of variable zones or similar zones obtained with a singlecouple/n-tuple or a small number of couples/n-tuples.

Position Measuring Point by the PSIT Method

PSIT method can be used as a technique for measuring the position of ananoemitter with high precision by using a different measuring mechanismand complementary to the method of the centroid.

Consider a nanoemitter positioned at the position x, y in Cartesiancoordinates and ρ, θ in polar coordinates. A sequence of illuminationconsisting of a fundamental wave, and a couple of the so-called“half-moon” distributions aligned along orthogonal axes is projectedonto the nanoemitter.

The pre-processing procedure created two images:

A “top hat” image consisting of the sum of the three images of thesequence and a vortex image consisting of the sum of the two half-moonimages.

A first descriptor is the Cartesian position is calculated using thealgorithm of the centroid of the image “top hat”.

Referring to FIG. 10, the radial position p can be measuredunambiguously by measuring a parameter, ρ_(a), equal to the arctangentnormalized by a factor π, of the intensity ratio between the normalizedintensity emitted by illuminated by the nanoemitter wave vortex, I_(v),and the normalized intensity emitted by the nanoemitter illuminated bythe fundamental wave, I_(F). In fact:

-   -   the normalized intensity emitted by the nanoemitter illuminated        by the fundamental wave varies from 1, at the centre of the        fundamental wave, to 0, at radius of Airy,    -   the normalized intensity, emitted by the nanoemitter illuminated        by the vortex wave varies from 0 for the centre of the vortex to        1 at the vortex maximum and reach 0 to a value slightly higher        than the radius of Airy. The arc tangent of the ratio is a        monotonic function.

The azimuth position can be measured by measuring the intensity ratiobetween the total intensity emitted by the nanoemitter illuminated bythe first half-moon distribution, I_(H), and the total intensity emittedby the nanoemitter illuminated by the second half moon distribution,I_(ve). The ratio between these two intensities is a geometric tangentsquare law:

$\begin{matrix}{\frac{I_{VE}}{I_{V}} = {\tan^{2}\theta}} & \left( {{EQ}.\mspace{14mu} 12} \right)\end{matrix}$

Both measures are redundant. This redundancy is a measure to qualify theobserved object as a single point and separate it from other objectspotentially present in the sample.

Direct application of the use of the PSIT method according to anembodiment of the invention for measuring the position of a nanoemitterwith high precision is the integration of this measuring technique intoa novel technique for local stochastic optical reconstruction. One ofthe limits of the applicativity of stochastic techniques is themeasuring process, needing a large number of images and therefore longmeasuring time and strong phototoxicity. Use of the PSIT techniqueaccording to at least one embodiment of the invention, which measuresthe position of a light emitter, at a resolution well above the Airydisk, at rates from micro or nanoseconds enables extension of stochastictechniques to many novel applications.

The images resulting from use of the PSIT method can also be processedusing the generalised Hough method, for recognising structured objects,line, circle or other, in an image.

Recognition and Measurement of Two Points: a New Resolution Criterion

Consider now two nanoemitters of the same intensity positionedsymmetrically about the centre at positions, ρ, θ and ρ, −θ in polarcoordinates. We will use the system described in the previousparagraphs. Three descriptors give the following results:

-   -   The centroid measure the centroid of the light distribution,        which will be the origin,    -   The identifier ρ, measure the value of the common radial value        of the two nanoemitters,    -   The θ descriptor, which in the case of half-moons contains a        degeneracy between θ and −θ, will measure the value θ.

As mentioned above, if the value of the descriptor ρ is not zero, weknow that the case study is not a point but two or more. In addition,descriptors ρ and θ allow us to measure the characteristics of the twopoints at a much higher resolution than that defined by the Rayleighcriterion. Moreover, using a compound process it is possible to separatethis case from the vast majority of cases of three or more points. Anadditional light distribution can be projected on the sample, ahalf-moon inclined at an angle θ; the assumption of the presence of twopoints will be confirmed or refuted based on the results of this image.Indeed, the measured energy will be zero for two points, for a line orfor a series of dots aligned in the direction of the angle θ.

Measuring is not limited a priori. Of course, there is at first apractical resolution limit, linked to the quality of the signal,fluctuations and various imperfections. If practical limits areneglected, the resolution limit is associated with the number of photonsdetected.

In practice, the resolution of a system using PSIT and/or PDOStechniques therefore depends on the sample observed. For a samplesparsely marked (i.e., such that the fluorescent markers are positionedon non-dense structures of wall, membrane, filament, specific sourcetype), the resolution obtained can exceed substantially the factor 2(locally or even overall).

Dark Tracking

Conical diffraction could apply a whole family of superresolution orsuperlocation techniques, the location of a single molecule. Referenceis now made to FIG. 8 which schematically illustrates an originaltechnique known as “Dark Tracking”.

In reference to FIG. 8, 80 represents the initialisation phase, i.e.,detection of the emitter using a confocal scanner or any other knownoptical method. 81 represents the positioning phase of the beam vortexon the emitter; 82 represents the case where the emitter moves relativeto the centre of the vortex and is excited by a fraction of the beamcreating fluorescence which can be detected; 83 represents therepositioning of the emitter at the centre of the beam vortex such thatno fluorescence is created and detected (recorded position Xi,Yi) and 84corresponds to a retroaction loop in which an independent locationsystem repositions the element followed by a corrected position.

The light distributions used by this technique are vortices generated byconical diffraction. However this technique can utilise other vorticesor other distributions generated by conical diffraction. It is suppedthat the molecule of interest has been marked by one or morefluorophores which can be excited at λ. The position of the molecule isfirst detected by a classic confocal image at λ. The position of thescanner is then adjusted to stimulate the sample such that the centre ofthe vortex coincides exactly with the position of the emitter. Thefluorescence signal is detected by a highly sensitive camera (ex. EMCCDor sCMOS), or PMT, enabling detection of the signal of low amplitude ofthe emitter by way of considerable quantic efficacy. The locationprocess is based on the absence of fluorescent signal when the emitteris exactly at the centre of the vortex. The fact that the intensitygradient is considerable near the centre of the vortex allows preciselocation of the emitter. If the emitter moves slightly the intensity itabsorbs will no longer be zero, and it will emit a fluorescence signalwhereof the position and intensity are deduced from the image. Aretroaction loop recentres the vortex on the emitter and saves theposition of the emitter. The retroaction loop can be executed at thespeed of execution of the camera (up to 1 kHz) or the detector (severalMHz), which tracks a molecule in real time and over an ensuing period oftime. Since the aim is to always minimise signals emitted influorescence by minimising the signal exciting the emitter, the locationcan be led over a long time period, with bleaching being less likely tooccur with such small doses of light. The precision of the locationdepends largely on the signal to noise ratio of the image, consequentlythe background noise (noise of the camera and self-fluorescence signal)must be considered. Suppose now that the sample is marked by twodifferent fluorophores which can be excited at two differentwavelengths, λ₁ and λ₂. Two beams with different topologies which dependon their wavelength are propagated together. The first (λ₁) has aclassic Gaussian form and produces an overall confocal image of thesample. The second (λ₂) is a vortex beam used for Dark Tracking. Bycontrolling the galvo mirror which scans the sample dark tracking can beperformed each time a line for the image camera is scanned such that theposition of the emitter is followed by a frequency much higher than thenumber of images per second. The main advantages of this technique,compared to another technique for tracking a single molecule, are theuse of a single scan system and the power sent to the tracked moleculesis extremely low. In practice, the use, alignment and shaping of thesetwo beams is not a trivial task if conventional techniques for beamshaping are used, such as holograms generated by computers, spatialmodulators or spiral wave plates, principally due to their inherentchromaticity. Conical diffraction can be used to simplify assembly. Byusing adapted optics a crystal can be adapted to generate a vortex withone wavelength and a Gaussian beam with another wavelength following thesame optical path. This uses a simple optical path starting out from afiber which resolves many practical problems. Dark tracking technologycan be easily used to study a number of biological questions in whichconventional tracking techniques of the position of a particle arepenalised by bleaching of the particles.

Dark tracking has been described hereinabove in the case of use of avortex. However, many variants using one or more distributions, forexample but not limited to half-moons or Stokes vectors, or anydistribution having zero intensity and a gradient—if possible thestrongest possible—as a function of one of the spatial dimensions, cancarry out Dark Tracking and are considered part of this invention. Thecapacities of conical diffraction for creating many different lightdistributions make it a tool of choice for performing Dark Tracking.

Reference is now made to FIG. 6b which is a simplified schematicillustration of a modified LatSRCS optical module, achromatic or not,700, according to an embodiment of the present invention. This modulediffers from the implementation of a LatSRCS optical module, 700,described previously and shown in FIG. 6a by the addition of severalelements before the module:

-   -   lasers 79 a, 79 b and 79 c optionally at different wavelengths,    -   fiber optics 78 a, 78 b and 78 c coming from lasers 79 a, 79 b        and 79 c,    -   optionally, polarization control sub-modules 77 a, 77 b and 77 c        for statically or dynamically modifying polarization of the        lasers 79 a, 79 b and 79 c, the polarization control sub-modules        able to be positioned before or after the fiber; however, in        some implementations, for example using PM fibers, “polarization        maintaining”, the polarization control sub-modules 77 a, 77 b        and 77 c may not be necessary and polarization of the light        coming from the fiber is determined by the relative position of        the laser and the fiber,    -   a laser combiner, 76 a combining two or more source lasers        optionally via fiber optic, 78 a, 78 b and 78 c into a common        output fiber 76 b,    -   an optical element 75 for transforming light coming from the        fiber into collimated light which can be used by the rest of the        LatSRCS module, 700, similarly to that described previously.

Many variations of this device, known to those skilled in the art, canbe added to this scheme and are claimed in this invention: for example,the two optical elements 31 and 75 can be integrated into a singleelement, or even removed if the output parameters of the common fiberare adequate. Similarly, the common fiber, 76 b, may not be necessaryfor some implementations.

In addition, the introduction, via a common fiber optic or directly bylight spreading in space of two or more wavelengths having differentpolarizations produces a method and/or a device capable of performingRESOLFT or STED techniques in all their different modalities. In thismethod and/or device the excitation and depletion waves spread along acommon path and the LatSRCS module 700 can be totally achromatic, or notin a simplified version, such as described previously.

In the simplest variant of this method, the excitation and depletionwaves spread along two linear orthogonal polarizations and a quarterwave plate—optionally achromatic—is positioned at the entry of thesystem to transform these polarizations into circular orthogonalpolarizations to obtain a fundamental wave for one and a vortex for theother.

In a novel variant of this method, the method integrative with uniquepolarization, described in detail later, the fiber is a birefringentfiber and creates a path difference greater than the coherence length ofthe depletion laser, creating incoherent superposition of the twoorthogonal polarizations. Another solution is the use of a polarizationsub-module (not shown), for example comprising a thick uniaxial crystalwith strong birefringence. Also, in the integrative method at the samepolarization a polarization sub-module, (not shown), for control ofintensity ratio can be used. This polarization sub-module for control ofintensity ratio is different to the previous polarization sub-module,but can potentially be integrated with it. It can potentially also beintegrated into the laser combiner, 76 a, positioned between the laserand the fiber optic. This polarization sub-module for control ofintensity ratio can be used to control the intensity ratio between thetwo polarizations, and therefore, as will be described later, theintensity ratio between the 2D depletion beam (vortex) and the 3Ddepletion beam (black sphere).

Reference is now made again to FIG. 6 b. The polarization controlsub-modules 77 a, 77 b and 77 c, can be activated to createsimultaneously sequences of light distributions, identical or different,for the excitation path and the depletion path. Also, the intensity oflasers can be modulated, creating a complex chronogram of the intensityof each laser, the sequence of excitation light distributions and thesequence of light depletion distributions.

In the preferred implementation, using a confocal microscope and anoriginal or modified LatSRCS module, achromatic or not, the followingare projected sequentially:

-   -   In first place an Airy distribution or an excitation fundamental        simultaneously with a depletion vortex. The resulting emission        image will be called the positive image.    -   In a second step, an excitation vortex, simultaneously with a        depletion vortex. The resulting emission image will be called        the negative image.

In a variant of the first step only one Airy distribution or oneexcitation fundamental is projected.

The image difference, consisting of weighted subtraction of these twoimages. However, this image difference can be digital processing moreevolved than simple arithmetic difference and can incorporate a set ofmathematical processing known to those skilled in the art for optimisingthe image resulting as a function, for example but non-limited, of thefrequential content of the two images. If good parameters are selected,this image difference will have a size—in PSF terms—finer than a classicSTED, needing only weaker depletion intensity. In fact, the aim ofdepletion of the vortex will no longer be to reduce the size of an Airypatch, requiring substantial energy, as in the classic STED or RESOLFT,but to reduce the surplus energy present in the excitation vortexrelative to the Airy distribution or the fundamental. Also, depletion ofthe Airy or the fundamental will be associated with subtraction of thenegative image created by the excitation vortex, equivalent tomathematical subtraction of two illuminations. The resulting reductionin size of the PSF will be the conjugation of these two effects.

Also, in some cases this embodiment can dispense with the need totrigger excitation as necessary in the “Gated STED”. In fact, photonsarriving before complete application of depletion can be considered byadequate choice of parameters without needing the addition of a complexand restricting system. Finally, the need to modulated STED, “ModSted”can also be avoided as the emission photons emitted by the depletionvortex hardly differ from those emitted by the excitation vortex and canalso be compensated.

In a second embodiment, using a confocal microscope and an original ormodified LatSRCS module a sequence of excitation beams, a sequence ofdepletion beams are projected simultaneously, the two sequences of beamsable to differ by their polarization, creating light distributions ofdifferent topologies. This device produces a sequence of lightdistributions of sizes less than those which would have been obtainedwithout the depletion beam. The SRCDA algorithm will be used in thisimplementation to determine the spatial distribution or the position ofspecific emitters. This embodiment, combining depletion and optics couldallow an adequate compromise between the intensity of the projecteddepletion beam and the gain in resolution.

In another embodiment, using a confocal microscope and an original ormodified LatSRCS module an excitation beam, in the form of an Airy and adepletion beam in the form of a vortex are projected simultaneously, thetwo beams differing by their polarization. Without dynamic elements thisdevice creates a fully achromatic STED device.

Use of Distribution of Helicoidal Symmetry for the 3D STED

The solution implemented in STED or STED-3D systems uses opticaldistribution of zero intensity at the central point and remains zeroalong the axis, over a certain distance. Use for the STED-3D is proposedhere of distribution having a position of zero intensity, this positionof zero intensity having a helicoidal spatial variation as a function ofthe axial parameter. The preferred implementation of this distributionis use of conical diffraction by using optical distributions asreferenced under the name of Stokes distribution. These distributionscould be performed, in particular though not exclusively, by usingtechniques based on the devices cited earlier, including but notexclusively the SLM (Spatial Light Modulator) and segmented mirrorswhich produce distributions of phase and/or amplitude in the pupil. Theuse of distribution of helicoidal topology to create distributioncontaining zero intensity having helicoidal movement is said to formpart of this invention. In particular implementation of thesedistributions by means of conical diffraction is one of the preferredimplementations of this invention, but the implementations of thesedistributions by means of a SLM or a segmented mirror to createdistributions of phase or amplitude in the pupil are also considered asone of the implementations described in this invention.

In a novel variant of this method, the integrative method of twopolarizations, the parameters of the crystal are selected such that thefundamental wave creates a black sphere and the wave vortex creates avortex. In these conditions, the two distributions, polarizedorthogonally do not interfere and, with a single input beam, anincoherent superposition of both beams independently creates the twobeams necessary for the STED 3D, the vortex and the black sphere. Thepossibility of creating the two beams by means of a single depletioninput beam considerably simplifies the optical system. Also, as thissystem has a common path, it can be executed simply. A polarizationsub-module (not shown), static or dynamic, positioned between the opticfiber and the crystal can be used to control the intensity ratio betweenthe two polarizations and therefore the intensity ratio between the 2Ddepletion beam (vortex) and the 3D depletion beam (black sphere).

In a novel variant of this method and such as described previously, theintegrative method of single polarization, a birefringent fiber—or apolarization sub-module—earlier created a path difference greater thanthe length of coherence of the depletion laser, for a CW laser, and/orthe time of the drawing, for a drawn laser or for the gated STED,creating incoherent superposition of both orthogonal polarizations. Inthese conditions, the two distributions do not interfere; as the twodistributions are orthogonal polarizations they will create on the samepolarization, one a fundamental—which by choice of parameters of thecrystal and of the optical system will be a black sphere, and the othera vortex. These two beams, derived from two incoherent distributions, asdescribed earlier, do not interfere; with a single input beam, beforethe fiber, this device independently creates the two beams necessary forthe STED 3D, the vortex and the black sphere. The possibility ofcreating the two beams by means of a single depletion input beamconsiderably simplifies the optical system. Also, as this system has acommon path it can be executed simply. The differentiation between thesetwo variants is in the output polarization of the two distributions, theblack sphere and the vortex, which are orthogonal in the integrativemethod having two polarizations and identical to the integrative methodhaving single polarization, each of the two variants having advantagesfor certain configurations.

In a novel variant of this method, using the conical diffractioncompatible with all devices described previously, and potentiallycomplementary to the two integrative methods, having two polarizationsand single polarization, the element of conical diffraction is replacedby a sub-module consisting of two crystals of conical diffractions, ofsubstantially equal value of the parameter of conical diffraction,separated by a polarization sub-module. The polarization sub-module isselected such that at the depletion wavelength, the polarizationsub-module has no effect, and the action of the crystals is added,creating the vortex and/or the black sphere. At the excitation lengththe polarization sub-module creates rotation of the polarization by 90°or 180°, the effect of the two crystals is subtracted, and thetransmitted beam is identical to the incident beam. This device preventscreating distributions which are too “exotic” on the excitation beam. Insome devices the crystals could have different values of the parameterof conical diffraction to also create an effect on the excitation beam,but with a value of the parameter of conical diffraction different tothat of the depletion beam. This variant can achieved at severaldepletion and excitation wavelengths by using the resources ofpolarization modules well known to those skilled in the art.

In a novel variant of this method, using conical diffraction compatiblewith all devices described previously, and potentially complementary tothe two integrative methods having two polarizations and singlepolarization, and compatible also with the preceding implementation withreasonable modifications, the element of conical diffraction is replacedby a cascade of crystals having different spectral properties such asthe LBO and the KTP (KTA) so as to enable realisation of a black spherehaving several depletion wavelengths. In effect, the dispersion of theparameter characteristic of the effect of conical diffraction, ρ₀, failsto achieve some distributions having several wavelengths, in particularthe black sphere, the form of which depends greatly on this parameter.The compensation of the dispersion of the characteristic parameter ofthe effect of conical diffraction, ρ₀, therefore enables realisation ofa 3D STED of common optical path, having two or more wavelengths.Further still, the compensation of the dispersion of the characteristicparameter of the effect of conical diffraction, ρ₀, can be achieved overa wide range of wavelengths either as described previously by acombination of crystals, or by spectrally correcting the optical systemto the second order, i.e. by creating a digital opening dependent on thewavelength to either compensate the dispersion of the parametercharacteristic of the effect of conical diffraction, ρ₀, or correctcompensation of the dispersion of the parameter characteristic of theeffect of conical diffraction, ρ₀, created by a combination of crystalsdescribed previously.

In another embodiment, using a confocal microscope, an original ormodified LatSRCS module and a LongSRCS module a sequence of excitationbeams, a sequence of depletion beams are projected simultaneously, thetwo sequences of beams able to differ by their polarization, creatinglight distributions of different topologies. The LatSRCS module producesa sequence of light distributions of sizes less than those which wouldhave been obtained without the depletion beam. The LongSRCS moduleimplements the PDOS method so as to separate collimated light ondifferent detectors, emerging from nanoemitters positioned on the focalplane of the objective lens, the non-collimated light emerging fromnanoemitters located on the near side of or beyond the focal plane. ThePDOS method in this implementation acquires essentially longitudinalinformation, i.e., the longitudinal position of each of thenanoemitters, complementary to lateral information obtained by means ofthe original or modified LatSRCS module.

The SRCDA algorithm will be used in this implementation to determine thespatial distribution or the position of specific emitters.

In another embodiment using one of the implementations described earlierand using a biaxial crystal to create the beam shaping, a dynamicpolarization element is used before or after the biaxial crystal tocorrect the dynamic movement of the pupil which in some cases can becreated during optical scanning of the confocal microscope. This effectof movement of the pupil is in some implementations of STED technologiesone of the performance limits, without needing an additional scanningsystem. [35]

In another embodiment using a confocal microscope, two or more lightdistributions locale at different wavelengths are projected by means ofan original or modified LatSRCS module. The first light distributionmakes the scene sparse, i.e., isolates emitters by means of a physicaleffect, which dilutes the density of emitters capable of emittingfluorescence so as to create regions in which the sparsity hypothesis isvalid, i.e., the presence of an isolated emitter or a small number ofemitters. The physical effects which will produce this sparsity will bethe same or will be derived effects, effects utilised to create sparsityfor location microscopy techniques of single emitters. These techniquescomprise for example PALM STORM, DSTORM, FPALM techniques and others.The second light distribution at another wavelength will producefluorescence whereof the intensity will vary over time. This secondlight distribution will use one of the PSIT techniques, either asequence of discrete distributions or a sequence of continuousdistributions. In the case of discrete distributions, light will bedetected either by a matrix detector or by a single detector. In thecase of continuous distribution, even though it is also possible to usea matrix detector, the most probable implementation will be the use of asingle detector; in this case the lateral information on position xy andpotentially the longitudinal distribution information z could beobtained by ratios of intensity. One of the most interesting cases isthe case of harmonic distributions over time in which electro-opticalcells are actuated by sinusoidal voltage. In this case the position xycan be rediscovered by means of measurement of the temporal harmonics ofthe signal measured by the detector, which can be a single detectorindirectly containing the information of lateral position.

Two crystals mounted in cascade (following each other) create anaddition effect of effects of crystals (if oriented in the samedirection), as described in Reference 46, or subtraction (if oriented at180°). Adding a rotator between the two crystals, turning thepolarization plane by 180°, reverses this effect creating a subtractioneffect in place of addition. In the case of a system having twoidentical crystals, using the addition effect of effects of crystals canhave two crystals whereof the effects are added. Using a chromaticrotator which turns at different angles, ideally at angles beingdifferent multiples of 180°, at different wavelengths, can have a modulein which the effects of two crystals are cancelled out at a wavelengthand are added to the other wavelength. The rotator in question can be asingle crystal (ex: quartz) whereof the thickness is optimised as afunction of the rotatory powers of the crystal at two wavelengths ofoptimisation to obtain a difference in rotation of 180° between the twobeams. In the case of a system having two conical crystals two biaxialcrystals of different material can be used; if subtraction of theeffects of crystals is used and if these effects depend on thewavelength differently for the two crystals, the module can be optimisedto have two crystals whereof the effects are cancelled out at onewavelength and are not cancelled out at another wavelength. This processof systems having N crystals whereof the effects are compensated oradded can be generalised to optimise the parameter ρ₀ for N wavelength.

The energy ratio in the 3D STED created by a conical crystal is fixed,the energy of the vortex being borne by (circular) polarization and theenergy of the black sphere being borne by the other polarization. Use ofa dichroic element—in the first dichroic direction or an elementselectively absorbing the polarizations—modifies this ratio. Thiselement can be either a circular dichroic element or a linear dichroicelement needing the addition of a polarization element before andoptionally after the dichroic. Dichroic elements representative butnon-limiting are Brewster plates or some dichroic glasses comprisingelongated metallic nanoparticles oriented homogeneously, enclosed insuperficial layers of glass.

Many other implementations of this general method will be clear to thoseskilled in the art, for example:

-   -   Some of the distributions created by the LatSRCS module, 700,        are superoscillations. In FIG. 7 b, the cases in FIGS. 7b ₀₀ and        7 b ₁₁ are superoscillations. It consists of a naturally small        spot enclosed by a wide and intense ring. As it projects a        depletion ring onto this superoscillation, it will be possible        to prevent, at an energetically low cost, fluorophores contained        in the ring from emitting and the size of the spot will be the        size of the central spot of the superoscillation    -   The creation successively or simultaneously of two—or        more—depletion light distributions can advantageously replace        the depletion vortex in all RELSOFT or STED modalities. One of        the possible effects is improvement in the form of the depletion        light distribution given the vectorial effects. It is also        possible to create a number bigger than 2 of distributions        called “half-moons” to explore different states of polarization.

Alternative Implementations

The embodiments of the invention described can be integrated on afluorescence confocal microscope. Superresolution system according toembodiments of the invention is a new method of measurement, in additionto or in replacement of existing methods of microscopy. However, thesuperresolution system according to embodiments of the invention mayequally be integrated on other microscopy platforms. These microscopyplatforms, as described as examples, include but are not limited to:wide field microscopes, dark field microscopes, polarizationmicroscopes, phase difference microscopes, differential interferencecontrast microscopes, stereo microscopes, Raman microscopes, microscopesdedicated to a specific task, such as live cell imaging, cell sorting,cell motility or any other instrument optical microscopy.

In another embodiment the microscope platform which has been describedis coupled to an electronic microscopy system (CLEM—Correlative LightElectron Microscopy), or any other similar system such as TEM(Transmission Electron Microscopy), or EBM (Electron Beam Microscopy),or SEM (Scanning Electron Microscopy).

In another embodiment of the invention, the microscope platform is acomplete SRCDP platform, and comprises a LongSRCS module, implementingthe PDOS method and using the SRCDA algorithm.

In another embodiment of the invention, the microscope platform is apartial SRCDP platform, and uses the SRCDA algorithm.

In another embodiment of the invention, the microscope platform is apartial SRCDP platform, and uses the control module.

In another embodiment of the invention, the microscope platform alsocomprises a LongSRCS module, implementing the PDOS method.

As to a further discussion of the manner of usage and operation of theinvention, it should be apparent from the above description. Therefore,any discussion on the form of the use and operation will not bedescribed.

In this respect, before explaining at least one embodiment of theinvention in detail, it is understood that the invention is not limitedin its application to the details of construction and arrangements ofthe components set forth in the following description or illustrated inthe drawing. The invention is capable of other embodiments and can bepracticed and carried out in various ways. In addition, it is understoodthat the phraseology and terminology employed herein are for the purposeof description and should not be regarded as limiting.

References cited herein teach many principles that are applicable to thepresent invention. Therefore, the entire contents of these publicationsare incorporated herein by reference, as appropriate to the teachings ofadditional or alternative details, features and/or technicalinformation.

The advantageous use of fiber optics is transmission of the fundamentalmode, TEM₀₀ mode and only it. However, some configurations of fiberoptics, mainly, though not exclusively based on fibers called “PhotonicCrystal Fiber” enables transmission simultaneous or not of more complexmodes, including vortex modes. It would therefore be possible to deportthe optical distributions created by conical refraction by means offiber optics, enabling major simplification of the optical system.

Also, some fibers “dual-core photonic crystal fibers”, [16], allowinteraction between two modes, one of them being a vortex, and providean additional physical mechanism to create diversified transferfunctions.

Many superresolution techniques are based on measuring point sources ofa size less than a wavelength fraction. The superresolution techniquesaccording to embodiments described enable measuring of point sources,but also of structured objects, for example and mainly segments oflines, circles or even continuous objects. In Biology, this extensionwill allow measuring of major biological entities such as filaments,neurones and some microtubules.

Even though the descriptions of embodiments, to simplify comprehensionof the invention, present applications in Microscopy, more specificallyin Biology, and even more specifically in Fluorescence Biology,applications can be extended to general applications of Microscopy andto the whole field of Vision, including artificial Vision.

Embodiments of the invention can be applied, by selecting a differentoptical system, to many medical applications, for example but withoutbeing limited, to ophthalmologic observation. This field of applicationcorresponds to the measuring of biological or medical objects ofmicronic resolution, the resolution being between 1 and 10 μm.

Also, embodiments of the invention can be applied, as explained later,via fiber optics. This allows many additional applications, for examplebut without being limited, to gastric or gastroenterologicalobservation, and to observation of the colon and urinary tracts.

It is understood that the invention is not limited in its application tothe details stated in the description contained here or illustrated inthe diagrams. The invention is capable of other embodiments and beingpractised and carried out in various ways. Those skilled in the art willeasily understand that various modifications and changes can be appliedto the embodiments of the invention such as described previously withoutdeparting from its field of application, defined in and by the appendedclaims.

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1.-25. (canceled)
 26. An optical measuring process for determining atleast one of a spatial distribution and a location of a set ofre-emitting sources on a sample, each re-emitting source re-emittinglight as a function of light projected onto the sample by a firstexcitation light distribution, the first excitation light distributioncreated from an excitation beam emitted by a first light source, whereofa wavelength of the first light source is aligned to an excitationwavelength of a re-emitting source of said set, the first excitationlight distribution being compact, projecting onto the sample the firstexcitation distribution; projecting onto the sample at least one secondlight distribution generated by a second beam emitted by at least onesecond light source, the at least one second light distributioncharacterized as a depletion or an activation distribution based onalignment of a wavelength of the second light distribution to adepletion wavelength or an activation wavelength of the set ofre-emitting sources, respectively; wherein each second lightdistribution is compact; wherein each second light distribution includesa superposition of a singular distribution characterized by a firstpolarization and one of a black sphere distribution and a top-hatdistribution characterized by a polarization orthogonal to the firstpolarization; wherein the first distribution and each seconddistribution spread along a substantially identical path from an outputof an optical bench to an objective lens of a microscope; wherein atleast one of the steps of projecting onto the sample the firstexcitation distribution and projecting on the sample each second lightdistribution is performed by means of an achromatic projection opticaldevice, the achromatic projection optical device based on conicaldiffraction or on propagation of light in a crystal; detecting lightre-emitted by each re-emitting source of the sample; generating at leastone image from the light in the step of detecting; and obtaining fromthe image at least one of spatial distribution information with respectto the at least one re-emitting source and a location of said at leastone re-emitting source.
 27. The optical measurement process according toclaim 26, wherein the first light source and the second light sourceinclude separate lasers.
 28. The optical measurement process accordingto claim 26, wherein the first light source and the second light sourceinclude a laser and a continuum source.
 29. The optical measurementprocess according to claim 26, wherein the first light source and thesecond light source include a laser and a continuum source
 30. Theprocess according to claim 26, wherein the crystal is uniaxial.
 31. Theprocess according to claim 26, further comprising separating lightemergent from two crystals by means of a polarization control element.32. The process according to claim 31, wherein the step of separatinglight emergent from two crystals includes passing light through anoptical element comprising a set of at least one achromatic quarter-waveplate and a chromatic wave plate, such that the optical element creates,between two conical crystals or between two uniaxial crystals, adifference in rotation of polarization between the excitation beam andthe second beam between 150 and 180 degrees.
 33. The process accordingto claim 31, wherein the step of separating light emergent from twocrystals employs a polarization control element whereof the material hasa property of optical activity and the thickness of the polarizationcontrol element is selected such that natural dispersion of opticalactivity of the material creates, between the two crystals, a differencein rotation of the polarization between the excitation beam and thesecond beam between 150 and 180 degrees.
 34. The process according toclaim 31, wherein wherein the step of separating light emergent from twocrystals includes providing crystals made of two distinct materials andcompensating conical diffraction approximately at the excitationwavelength by natural dispersion of the two distinct materials.
 35. Theprocess according claim 26, wherein the excitation distributioncomprises one of a Gaussian distribution and an Airy spot.
 36. Theprocess according to claim 26, wherein at least one of the first lightsource and the second light source comprises a laser.
 37. The processaccording to claim 26, wherein the first beam is characterized by apolarization that is one of linear and circular polarization.
 38. Anoptical measuring process for determining one of a spatial distributionand a location of re-emitting sources disposed on a sample, whereinre-emission by each re-emitting source is determined by a law relatingreemission of light as a function of light projected onto the sample,the optical measuring process comprising: projecting light onto thesample by means of a projection module, the light characterized by awavelength aligned to an excitation wavelength of each re-emittingsource, such as to produce a sequence of compact light distributions ofmutually distinct topology; optically scanning the sample to a pluralityof scanning points; detecting light re-emitted by each re-emittingsource for each of the sequence of compact light distributions ofmutually distinct topology and for each of the scanning points;acquiring for each scanning point one of an image or a sequence ofimages, each image corresponding to a compact light distribution of adistinct topology; applying an algorithm in which formulation of thereconstruction of the sample and its spatial and/or temporal and/orspectral properties is considered as a reverse Bayesian problem andthereby defining a distribution a posteriori, by way of Bayes law; aposteriori combining a probabilistic formulation of a noise model andany Bayesian prior with a light distribution created in the sample byprojection; and representing results of a posteriori combining in one ofan image and digital and graphic data.
 39. The optical measuring processaccording to claim 38, wherein the step of projecting light includesemploying an achromatic projection module.
 40. The optical measuringprocess according to claim 38, wherein the algorithm comprisesestimating the light distribution in the sample by the use of clouds ofspecific emitters favouring sparse solutions; estimating an average aposteriori, and representing results, based on the average a posteriori,in one of an image and digital and graphic data.
 41. The opticalmeasuring process according to claim 38, wherein estimating of theaverage a posteriori is performed by means of an algorithm ofMonte-Carlo Markov Chain (MCMC) type.
 42. An optical measuring processfor determining one of a spatial distribution and a location of at leastone re-emitting source disposed on a sample, wherein re-emission by eachof the at least one re-emitting source is determined by a law relatingreemission of light as a function of light projected onto the sample,the optical measuring process comprising: projecting light onto thesample by means of a projection module, the light characterized by awavelength aligned to an excitation wavelength of each re-emittingsource, such as to produce a sequence of compact light distributions ofmutually distinct topology; detecting light re-emitted by said at leastone re-emitting source of the sample for for each of the compact lightdistributions of mutually distinct topology and for any scanning pointsof the sample; an image acquisition module for acquiring for anyscanning point, either an image or a sequence of images, each imagecorresponding to one of the compact light distributions of mutuallydistinct topologies; reconstructing the sample and of its spatial and/ortemporal and/or spectral properties based upon a reverse Bayesianproblem leading to definition of a distribution a posteriori, by way ofBayes law; a posteriori combining a probabilistic formulation of a noisemodel, and any prior on a light distribution created in the sample byprojection; applying a MAP algorithm; and representing results, based onthe MAP algorithm, as one of an image and a digital and graphic data.43. The optical measurement process according to claim 42, furthercomprising scanning the sample optically.
 44. The optical measurementprocess according to claim 42, wherein the MAP algorithm includesregularization with positivity constraint.
 45. The optical measuringprocess according to claim 42, wherein the MAP algorithm also contains afrequency band limitation restriction.
 46. The optical measuring processaccording to claim 42, wherein the MAP algorithm includes an accelerateddigital diagram of Nesterov type.
 47. The optical measuring processaccording to claim 42, wherein the sequence of images employs aredundancy in frequency information due to different frequencycharacteristics of different distributions projected onto the sample,for compensating any impact of missing points or scanningirregularities.
 48. The optical measuring process in accordance withclaim 42, wherein the MAP algorithm is adapted to resolve an inverseproblem relating to a sum of terms.
 49. The optical measuring process inaccordance with claim 48, wherein the terms include at least one of alow-frequency component and a sparse component that is sparser than thelow-frequency component.
 50. The optical measuring process in accordancewith claim 42, wherein the MAP algorithm is adapted to impose anon-local redundancy restriction on the solution.
 51. The opticalmeasuring process in accordance with claim 50, wherein imposition of thenon-redundancy restriction includes calculating weights on images or ondifferent digital masks and applying a non-local tree of similarities tothe solution as regularization.
 52. The optical measuring process ofclaim 42, further comprising using a mask of variable size in the planeof the detector to obtain images having either different axialcharacteristics, or different or optimised rejection capacities ofparasite light, overall or locally.
 53. An optical measuring device fordetermining the spatial distribution or the location of a re-emittingsource on a sample, the device comprising: a first light source, whereofa wavelength is aligned to an excitation wavelength of said re-emittingsource, the first light source adapted to project a compact excitationdistribution; a second light source characterized by a wavelengthaligned to a depletion or an activation wavelength of said re-emittingsource, the second light source adapted to project a second compactlight distribution, the second light distribution including asuperposition of a singular distribution of a first polarization, andone of a black sphere and “top-hat” distribution of a polarizationorthogonal to the first polarization; a projection module for theprojecting onto the sample the first excitation distribution and thesecond compact light distribution, the two distributions spreading alonga substantially identical optical path from an output of an opticalbench to an objective lens of a microscope; an achromatic projectionoptical device for projecting onto the sample the first excitationdistribution and the second compact light distribution, the achromaticprojection optical device being based on one of a conical diffractioneffect and a propagation-of-light effect in uniaxial crystals, theachromatic projection optical device comprising a cascade of at leasttwo conical or uniaxial diffraction crystals; a light detection modulefor detecting light re-emitted by said at least one re-emitting sourceof the sample; and an image generation module for generating at leastone image from the detected light to obtain, from the image, spatialdistribution information or location of said at least one re-emittingsource.
 54. An optical measuring device for determining at least one ofa spatial distribution and a location of a set of re-emitting sources ona sample, the device comprising: a first light source, whereof awavelength is aligned to an excitation wavelength of said re-emittingsource, the first light source adapted to project a compact excitationdistribution; a second light source characterized by a wavelengthaligned to a depletion or an activation wavelength of said set ofre-emitting sources, the second light source adapted to project asequence of compact light distributions of mutually distinct topology; ascanning module for scanning the sample optically; a module fordetecting the light re-emitted by said set of re-emitting sources of thesample each compact light distribution of mutually distinct topology andfor each scanning point of the sample; an image acquisition module foracquiring for each scanning point, either an image or a sequence ofimages, each image corresponding to one of the compact lightdistributions of mutually distinct topologies; and a processor adaptedto execute an algorithm in which formulation of the reconstruction ofthe sample and of its spatial and/or temporal and/or spectral propertiesis considered as a reverse Bayesian problem and leads to the definitionof a distribution a posteriori, by way of Bayes law, and a posterioricombining the probabilistic formulation of a noise model, as well as anya priori on a light distribution created in the sample by projection.55. An optical measuring device for determining one of a spatialdistribution and a location of a set of re-emitting sources on a sample,the sample comprising at least one re-emitting source, excited by lightprojected on the sample and re-emitting light according to a lawdetermined as a function of the projected light, the device comprising:a projection module containing a laser, whereof the wavelength isaligned to an excitation wavelength of said set of of re-emittingsources to create a sequence of the compact light distributions ofdifferent topology, a detection module for detecting the lightre-emitted by said at least one re-emitting source of the sample for theor for each of the compact light distributions of different topology andfor each of the scanning points of the sample; an image acquisitionmodule for acquiring for each scanning point either an image or asequence of images, for the sequence of images, each image correspondingto one of the compact light distributions of different topologies; analgorithm module in which formulation of the reconstruction of thesample and of its spatial and/or temporal and/or spectral properties isconsidered as a reverse Bayesian problem and leads to the definition ofa distribution a posteriori by way of Bayes law, and a posterioricombining the probabilistic formulation of a noise model, as well as anya priori on a light distribution created in the sample by projection, aMAP algorithm module regularized or not regularized with positivityconstraint; and a representation module for representing results, basedon the MAP algorithm, either in the form of an image or in the form ofdigital or graphic data.
 56. An optical measuring device according toclaim 30, wherein the projection module is achromatic.
 57. An opticalmeasuring device according to claim 30, further comprising a scanningmodule for scanning the sample optically.